It depends entirely on what the law says where you live. During my recent inpatient stay (last year) I was certified (e.g. involuntary) for most of my stay, but opted to stay as a voluntary patient a few more days. This was done because I was looking at getting into a treatment program that did not accept referrals for patients who are currently certified. Even before I was admitted to the psychiatric ward, I was treated for co-occurring medical problems in the emergency room, despite already having been certified. The only difference between involuntary and voluntary is that as an involuntary patient you can't leave.

It also seems extremely odd that they wouldn't treat wounds like you've described. If this was at a major metropolitan hospital, they should've had such care available 24/7. Even in smaller, regional hospitals, I'd have guessed such care would still be available on call.