Ok, so I don't have 50 reputation right now, so I'll just post a comment here: do you have to play the recorder while waiting for the injury to heal? It's most likely not as severe as trying to play with a broken arm, but imo it's comparable; if you try too hard to cover up the hole (there's definitely some pressure needed) and hurt your finger in the process that's no good. Also, is there a way to wrap something around the finger that can cause it to cover the hole more effectively?
Another question is whether you actually have to feel where the finger is on the recorder, since the left ring finger/fourth digit only has one hole to cover, and thus the movement of the finger can be muscle-memo'd, or you can just look at the fingers while playing. =P
Anyway, if you really want to continue playing recorder (which'd be fine, because music>no music) just don't hurt yourself further. :3
(Then of course there's the extreme recorder player who learns alternative fingerings for each note that requires that finger in the first place)