OP -
**If it's anonymous, contact your ombudsman, definitely be sure before you talk to them that nothing you say leaves the two of you without your permission
the ombudsman likely knows the dean and the culture of your particular school best and can probably offer you the best advice for smoothing this over
the job of the ombudsman is typically to be a confidential source of support to students and a neutral party in any issues involving students and admin
**I agree, writing an apology to everyone you offended is a good idea, I would sent it via email to have a record of what, when
**Definitely set up an appt with a psychiatrist AND set up some regular counseling ASAP! you want to have on record that you did that
I don't know that you should go to the Dean... do NOT ask the person you offended who said they would report you not to report you, that would unprofessional, but there's a chance that a sincere apology might make her not bother.
It's best if you can avoid their radar if someone else doesn't do it, and if they ask you why you didn't go to them first you can point to what you did to try to address the problem... at my school, they always encouraged that resolving conflicts with peers should always be attempted peer to peer and that going "above" someone in the hierarchy should only be done if successfully resolving an issue was not likely at the local level. Hence, your explanation would not include what I just said, I include this for why at some institutions trying to fix this with your peers and seeking help without making a point of going to the Dean would be an OK approach should you get hauled in.
Anyway, if you go that pathway and then are asked the question why you did not go to them, let them know that you recognized how unprofessional this was and went about rectifying it directly with your peers via apology and also took steps such as contacting the ombudsman and seeking professional help via counseling for introspection. Let them know you know how important professional reputation is in the field and know that what you did damaged your reputation, and you were trying to preserve your professional reputation by being proactive in this manner but that you were trying to keep this to the involved parties.
**Do not talk about this incident with any of your peers. If a classmate confronts you about it or the details, just say "yes, I acted unprofessionally and have taken steps to take responsibility for my behavior, apologize, and be more professional in the future." If pressed for more, say, "say, I'm sorry but this is an incident I think best left to those directly involved, and would like to leave in the past as I seek to rebuild my professional reputation."
I say talk to your ombudsman because at my school this sort of approach to fly under the admin radar and fix this would fly, they would respect what I outlined as appropriate steps but that you did not go to them off the bat, but it could very well be like what
@Goro and others are saying that you ARE better off being the one to cat-out-of-bag this to your Dean.