First thing is to get your wrists checked to make sure you don't have any structural problems that need to be corrected before you begin training. After that key is taking resistance off of the motions until you can build stregth. This can be accomplished a bunch of ways.
For push-ups, you can do them against a wall or other elevated object, gradually lowering the height of the object until you are on the floor.
With pull-ups, you can use a gravitron machine that takes resistance off by using counter weights. You can do jumping pull-ups where you use your legs to help you get up to the bar and lower yourself under control. You can then jump up to the flexed position and hang for time.
Also, a jump-stretch band looped over the bar works great. Loop it over the center of the bar and step into the loop of the band. It will stretch as you decend and assist you with the pull-up. Gradually use lighter and ligher bands as you get stronger.