Find a good gym. There are some gyms where the instructors (and consequently the students) are a bit too hardcore. But at the good gyms (which I'd say are actually the average in the community, not outliers by any stretch), no one wants to injure their training partner. I've got a bad shoulder and a bad back. When someone gets my left arm in certain positions, I tap quickly and no one gets upset. I tell my partners about it, and tell them they can grab it just go extra slow.

So far my only BJJ-caused back or shoulder injuries were from early on when I was either too inflexible (and so it was easy to push it too far), or too stupid to tap (hadn't realized what "too far" was). Take it slow, find good training partners, listen to your body, and take up complementary activities (some strength training, flexibility things like yoga, core training especially for the back).