Sorry to hear of your predicament. Here on tips on maintaining a "fool proof" restore and disaster recovery system. I talk about restore systems, not backup systems. The goal is restoring the data when needed with minimum loss. The philosophy is defense in depth.
For an in-depth teatment on this topic see PlotinusVeritas' excellent dissertation on this subject:
Ideal philosophy and security of your valuable data
https://discussions.apple.com/docs/DOC-6031
"Pros" maintain multiple backups, not just one, and not just two. The external media is cheap and the data is highly valluable so the equation is simple. You want multiple backups. You store only backup data on a backup volume.
You want to store at least one restore volume not in the same building as your Mac. This is for a marjor disaster recovery such as fire, flood, theft…
You also want to maintain the backups in two different formats: Time Machine backups and clone backups.
The beauty of Time Machine backups is they are easy to keep up to date and they are useful for going back into time for accidentally deleted or corrupted files. It will also backup multiple volumes (such as the internal disk/SSD and an external disk) as long as the restore volume is big enough to hold the data in use.
The downside of TM is its complexity. I have had TM restores fail and I was very glad I had a second copy.
The beauty of clones are their simplicity and immediate recovery. You can create clones with several software systems (including Disk Utility) but I prefer an inexpensive software system called Carbon Copy Clone. PlotinusVeritas introduced me to this recovery system recently in these Community postings and love it.
CCC will make a bootable copy of your internal disk. You get one copy as of the latest backup so you cannot go back in time but instead you have a very simple method to recover your data. For example if you have an internal disk (as opposed to an SSD) you simply replace your internal drive with the cloned drive and you are up and running immediately You can also plug it in as an external drive and boot from it immediately. It is less error prone than TM. The first time you run it, it does a full backup. In subsequent runs it copies over only files that have changes so it is a quick backup.
The downside of CCC is you usually run it manually. You can keep a clone disk plugged in and CCC will maintain a schedule when to backup (such as nightly).
So for a reasonably complete system you would have four backups: One TM and one CCC backup onsite and the one TM and one CCC backup offsite. Then occasionally swap the onsite and offsite disks to keep the offsite disks reasonably current.
When it is time to restore you have a choice. The TM backup will probably be more up to date than the CCC backup. So I usually start with a TM restore and if that does not work fall back to the CCC volume. If my CCC restore volume were reasonably current I would start with that. Others who don't trust TM as much as CCC and don't mind losing the updates that happened between the latests TM and CCC backups use the simpler and more immediate CCC restore. I start with a ™ restore with CCC as my fallback position.
May you recover your photos and then back them up with defense in depth.