I sometimes get usage bruises in my wrists (although I get them from mousing on my computer as well so I'm not sure how good of a measure that is). If you already have tendonitis issues, climbing will probably aggravate them. I don't have tendonitis issues and my finger tendons usually hate me after climbing. I tape as a preventative measure. Proper technique reduces problems in the wrists. Also, it helps to just accept that you are going to be where you are at in terms of climbing ability. Adjusting your climbing for your body is a time honored practice. There is someone at my gym who is only able to use one hand. I've worked on climbing without hands. There are ways to challenge yourself when climbing that don't involve harder and harder problems which means that there are ways to adapt climbing for almost everyone.

Climbing hurts. It does. Our fingers are raw. Our knuckles are cranky. Our forearms burn. We end up bruised and bleeding. Yet we still climb because it is worth it.