can I access my iphone photos on my computer

Follow the steps in this support article to start using iCloud Photos. There is also instructions on upgrading your iCloud storage if needed. You get 5GB free storage which is usually not enough space, depending on how many photos you have, but you can upgrade to 50GB storage for 99 cents/month. Once this is done on your Mac and iPhone, then any changes on one device will automatically be reflected on the other. You are correct that managing and organizing photos on the Mac is easier.

Set up and use iCloud Photos - Apple Support

As long as your Computer and iPhone are using the same Apple ID, your best option is to use iCloud Photos to sync both of your devices. The drawback is that you may need to purchase additional iCloud space to accommodate your photos, but this would allow you to organize your photos in Albums on either device and the changes would be reflected on the other. No additional syncing steps with your computer would be required with this approach and everything would happen automatically.