Well, if everything you care about was in your iPhoto library before all of this happened, the good news is that you have not lost your photos. The bad news is that retrieving them all out of the iPhotos database file (it's a container just like an app file is that you can open by right clicking and choosing to Show Package Contents) is going to be a pain in the rear because of the multitude of folders they will be nestled in which I believe all just have numeric names that will make no sense. You will have to open every single one of them and copy the files out so they can be imported again to Photos. This here is the worst case scenario but all things considered, it sure beats losing your precious photos. They are all inside of that iPhotos data file in tons of folders.
I think too based on the error you reported that your existing iPhoto hadn't been updated to the most recent version before 10.10.3 was installed which older versions are not compatible with. They won't open and there's no place now to download a newer one. So I don't think you'll ever be running that iPhoto app you have again unless you revert to an earlier version of OS X over it. I wouldn't bother myself but that's up to you.
I absolutely agree with the very sound advice to avoid system cleaning products, etc. The ones on the web are bad news as a rule. There are some light duty ones on the app store but really they are not needed. As mentioned above, the system does a good job of taking care of itself. There's no need to obsess over it and waste time and money doing so. It's designed so we don't need to do that.
I don't want to rub salt in the wound so please take this in the spirit in which it is intended, to help you. Before you do anything else about this at all, buy yourself a 1 TB USB 3.0 external hard disk which should run around $100. or maybe less on Amazon.com for example. I would recommend the Western Digital brand personally as I have found them to be Mac compatible whereas I had trouble with a Seagate that would not work properly with Time Machine even though it was branded as being especially for the Mac. They conceded the problem was on their end and offered me a refund to their credit but I would not go with them again after that. So that's my advice for a disk drive. Do yourself a huge favor and attend to this right now so that while working to fix this it becomes impossible to lose your photos. Time Machine works very well, is completely unobtrusive backing up in the background hourly or however you need to use it if on a mobile Mac and it is a very simple affair to recover lost files from previous daily, weekly and monthly backups as needed when a disaster like this strikes. Time Machine is the nicest, easiest, most reliable backup program I have ever used and I've been using personal computers since Apple IIs were around.
You will never regret the money spent on a backup drive to protect you against loss. Yes, you can put stuff up in the cloud but Time Machine backs up the entire system for you so no matter what gets screwed up, deleted or lost it can be recovered. So, I really hope you will do that for yourself so you never, ever have to deal with a situation like this again. Next time could be worse. What if the photos really were gone? Can you imagine? Don't let it happen to you.
So, in my opinion while it is going to be some work, the simple and foolproof way of recovering from this would be to run a full backup with Time Machine first. Then stash the existing Photos library file in case you wind up wanting it for something along the way here. Once you've made a copy someplace safe, trash the one in the pictures folder and fire up Photos to create a brand new empty one. Then make a copy of your iPhotos library file and stash the original someplace safe. These will already be in Time Machine at this point but I like to play it safe. With that done, right click the iPhotos library file and go about the business of navigating through all the folders within it, moving out all the photos you come upon as you go. Later you can import all of that into Photos which will using the metadata help organize it somewhat by dates, etc. and you can go from there. This is a pain but it is simple and guaranteed to work. It is not complicated. It is just work is all.
By the way, the reason I say to move the photos out of the iPhoto library is simply to help you keep track of what you are doing and so you will know for sure when you have gotten them all. To facilitate this once each folder has been emptied of the photos you want, delete it. Remember, we made a backup copy so we can do this stuff without worry and we also have it backed up on an external drive with Time Machine at this point. So you can do this stuff without worry to the extra copy of the library. In this scenario you have two other untouched copies to fall back on if anything goes awry but I don't see that happening.
Another word of caution. I would make it a routine to check for updates at least weekly so you don't miss any important ones like the iPhoto one you don't have now. You could use the Reminders app to make a little reminder to do it Fridays or something. This will help you a lot more than a destructive cleaning utility.
So I hope all that is helpful to you. I especially hope that you will take my advice to stop right now and attend to the Time Machine backup before doing anything else. Then you'll protect yourself against really losing them all somehow.
If you have a Mac using friend with the most recent iPhoto app, using a copy of that as directed above may be your salvation and save you the work I just outlined. However, if that is not an option the method I outlined above will work assuming nothing has been done to your iPhoto file to remove the photos from it which I very much doubt has happened here from what you describe.
By the way, meaning to help further here i just looked inside my stored away iPhoto library so i could tell you where your photos are. When you right click and choose "Show Package Contents" from the menu, the library file will be opened in Finder. You'll see a bunch of folders here and some files, etc. The folder you want to open at this point is called "Masters." This is where your photos live. Inside this folder you will find more folders, each one labeled by year for the year of all the photos in that particular folder. When you open one of those, the fun begins as you find number folders to open probably multiple levels deep until you arrive at one with a bunch of photos in it. That's all there is to it. You just keep moving through all the folders, moving out all the pictures and deleting each one when done to help maintain your sanity, I mean keep you place in what you are doing and that's that.
I hope that last bit makes things clearer and possibly takes a little fear out of this. Honestly, it isn't complicated after all you will find once you being finding and moving all your photos. And if you have the backup I've been harping on you about you won't have to worry about a thing while doing this nor in the future.
Don't feel too badly here. A lot of us, myself included, had to learn this by suffering disaster first too. You aren't alone there.
