Hand bleeding?

[Francis the Tegu]

My baby tegu is shedding at the moment and the "thumb" of his hand is bleeding. Not badly, but i picked him up and he got some blood on my hand. I really hope I didn't cause that, it possibly could have been him scraping his shedding off in the cypress mulch of his cage. Right now hes sleeping on my desk in my old jacket with his hand kept under his body. I really cant post pictures right now because I don't want to hurt him, or frighten him. He's still not used to me. Is there anything I can do to help him? Like give him a bath? Or will the water make it worse? He hasn't eaten anything since I got him a week or two ago, probably because of the time of year it is. So that won't help.
Please respond, I don't want him to be hurt

 

[Francis the Tegu]

Update: I was able to get a picture of his hand after he moved for a bit and went back to sleep.

 

[Walter1]

Clean with hydrogen peroxide. Then apply newsprint. Then check with vet. Looks swollen above.