As someone who spends a fair amount of time bent over a fender, this is a pretty common complaint. You are using muscles that are generally not used enough, and you get a strain. Others have voted for core conditioning, and it works. You need to build and exercise the muscles that you need to use regularly. I can work over a car now for hours without a lot of issues and I'm a lot older than you.
It's just that you stressed a part of your body that you haven't kept in condition and it's complaining. The simplest conditioning for lower back is to warm up, then put a few pounds in your hands and lace them behind your head, holding the weight to the back of your neck area. Not too much, just a couple pounds will do, maybe a bound copy of War and Peace - or, the federal register(kidding). Now, bend over about 90deg and hold it for a short time, then stand straight again. Bend, hold, stand. As you get stronger, add just a bit more weight, maybe 5-7lbs and go a bit deeper down to beyond horizontal.
When you bend and straighten, don't jerk back up. Move smoothly. You can also help by doing the same basic move to the left and right side, although you can't get all the way over to 90deg. After a few weeks of this your back won't bother you unless you really overdo it.