I started doing strength-training for the first time ever at age 44 (last year), so we’re in the same boat training wise.
I think flexibility is a key requisite to strength training, and I suspect that injuries are even more prone to occur when your CNS is afraid of a muscle being longer than it usually is. This can cause tension elsewhere and lead to injuries. You might be having problems because your body won’t let you do the things you’re trying to do; if your muscles seize-up accordingly, your risk of injury goes up.
“Stretching” has been mentioned by some of the writers (along with some other great ideas), but I suggest you go quite deeply into that area.
As well as conventional static stretches, I strongly suggest you go look at the other types of stretches. People talk about “dynamic” stretching, but to tell the truth, I couldn’t figure it out. However, Chad Waterbury indirectly led me to another web site where I found Pavel Tsatsouline’s e-books “Super Joints” and “Relax into stretch”. In these, he describes stretching techniques I was not aware of. I bought both ebooks and learned more about stretching there than anywhere else. Worth a look at least IMO.
Here’s a link to Pavel’s web site, moderators permitting:
Alternatively, I’m sure you can find him in a search engine near you…
Don’t give up! Clearly, you should go easy for a while with lighter weights and such, but improving flexibility is almost certain to help you. Good luck whatever you do.