First off, for your injuries you can work around them with certain exersizes. Some gyms have this machine for shoulders where you put you shoulders under these pads that you raise to the side, I forgot the exact name of the machine but anyway you dont have to use your thumb. With your chest you can use a pec deck where you place your elbows against the pads and bring them together. As for diet if you really want to bulk you will put on some fat. The first thing I would try is to increase you daily calories by 500-1000 and see where that goes. Also aim for about 275-300 grams of protien daily. make sure your foods are clean. See what that does for you.

Thanks for the help. The grip on my thumb isn't so much the problem as the palm. I wiped out skateboarding and the whole wrist/hand area is bruised and swollen. I've tried doing bench presses but I can barely put up an empty bar without there being pain.

Also, when you're bulking up, how much fat should I look forward to putting on? I've never done a bulking phase or anything. Would I put on 20 pounds or something, or is it more like a couple? It probably depends on my metabolism, but what's normal?

IMO it would depend on the individual and how far they would be willing to take it. You could bulk at a moderate pace gain a little more muscle and some fat or you can really pig out bulk up and put on lots of muscle with a good amount of fat. It depends which way you want to go.

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