My wrist is hurting? Assuming from too much exercise?

6 days a week I do 55 pull ups against the bath (I place my hands on the bath with my palms facing outward and drop myself down, I then use my upper body strength to push myself up). I have a shower then do another 55 of this exercise (I forget what they call them). About half an hour later I do 25 push ups. I have been doing these exercises for about 5- 8 weeks now (I increase the amount of bath pull ups and push ups by 5 each week).

Recently, my right wrist has started to Hirt whenever I do the exercises. I place my hands in an awkward position on the bath, that might be why. I also lean a bit onto my right hand when doing the bath pullups.

Why would my right hand be aching and what can I do to stop it?

Thank you