I apologize in advance for this answer being so long.
You really have two questions here. Yes, you're right, of course you need to tell your friends. You would want to know if a mistake like that had been made with your four-footed (or two-footed) child. If they are angry, well, you can't blame them because you are angry with yourself, so expect it.
Some close friends asked us to take care of their dog at our house for a few days (several years ago). He was a very tiny, happy little guy, and my friend even said he was so good at following people we would probably not even need a leash on him outside. So we ignored the leash... and he cut and ran! (We should have kept him on leash, whatever they said, because we already knew that dogs are very practical; they know that if they're with someone other than their person, they may not have to obey their person's rules!) It took almost two hours on a cold December night to find him - just after he had been run over and killed. He's buried in our back yard. We all are still friends - but they have never asked us to dog-sit since, and I still feel bad thinking about the whole thing.
So 'fess up and tell the truth and take your medicine. Afterwards, give or send the dogs a treat they enjoy (an approved type of bone, perhaps) or give your friends a gift card to the nearest pet supply store.
Now you need to do something about remembering. You're too young for Alzheimer's, but if you're really worried, you could talk to your doctor (who won't laugh).
Mothers have SO many things to keep track of that it's easy to mix them up. When my children were growing up, they earned a lot of nickels from me by finding where I'd left my car keys! What's worse, once (just once!) I was juggling so many things in my brain that I forgot to pick up my daughter at the orthodonist's; this was before cell phones, and it took her two hours to get hold of her dad to pick her up. Me? I was out running the rest of the errands I had to do that day! Forgetting one's children is truly embarrassing!
That fact is that our brains start traveling in too many directions.
I suggest you revert to a very old-fashioned system, at least for the next six months. Get out to the store this weekend, buy a one-year paper calendar, AND put it up on the wall of your kitchen. This is so the calendar can't run away to anyplace else in your house (making you wonder where IT is). It doesn't have to be fancy, but it has to have spaces big enough to write several things down by each date. Get a pen with a cap, and fasten the cap with a string to the same tack that holds the calendar.
Now, whenever you have ANYTHING specific to do - from pet-sitting to some sort of appointment to somebody's birthday - WRITE IT DOWN on the calendar immediately! It will take a few days to get into the habit, so start right away. Let it be your brain for these matters. Get everything down on paper. Those little blank spaces will fill up quickly, and you can refer to your calendar every time you walk past.
If you feel you need something like that when you're away from the house, get a pocket calendar or just a purse-sized notebook. Keep a pen attached to it and WRITE EVERYTHING DOWN - even things you're sure you won't forget. This is training, remember.
Think of this old-fashioned calendar as a personal assistant. While you do things that only you can do, you've delegated to your assistant the job of keeping track of appointments and events. All you need to do is to check with it - and there it is, right in plain sight.
I do a lot of work on my computer, and I keep a pad of sticky notes there. When I think of something else I need to do, I jot it down, stick it where I can see it, finish what I'm doing, and then deal with my sticky notes.
Pick a specific, easy place in your house where you will always put your car keys when you come home. If you can, put a little dish there so you can plunk your keys into it every time. I recharge my cell phone in the same place I put my keys.
Depending on how your house is set up, pick your desk or somewhere else as the dedicated spot for papers - put them there right away and work on them there. You can't take care of the papers right away, but you can train them to wait for you in the area where they should be.
After six months, check how you're doing. Is life easier? Are THINGS more manageable? Are you getting done what needs to be done? Would a different kind of calendar work better for you? My daughter uses a dry-erase type, but that doesn't work for me because I schedule things more than a month in advance. Some friends use their fancy cell phones with the appointment calendars, but I don't keep my phone on my person when I'm at home. If you realize that another type of assistant would work better, "hire" that one. But if the paper calendar is working, keep with it.
Hope this helps. Start now and soon you'll have developed a good system that serves you well.