If you are really worried about your degu you should go to a vet.
Because the wound is in such a sensitive area I would suggest going to a vet. Also, he/she isn't active which could mean that it's bad. Don't let him/her have a dustbath because the dust could get in the wound and make it worse... take out the sticks too!
Since you have them separated, make sure you keep their cages close together so they can smell each other that way you dont have a problem reuniting them after he/she gets better.
If for some reason you choose not to go to the vet make SURE you keep a close eye on the wound! At LEAST check it twice a day and make sure it doesnt get worse (puss, redness, any other bad things). You can also put neosporin (polysporin) on it which might help (or you could even use a saline solution).
I hope your degu gets better soon, and i would really suggest taking him or her to a vet!