Chances are that this case is going to be adjourned in contemplation of dismissal or you will be offered a disorderly conduct
, which is a violation and not a crime. Either way there is likely to be a community service requirement, but if you have a health issue you might be able to avoid that altogether if you're willing to pay a heavier fine.
The problem is that DAs in NY won't negotiate with unrepresented defendants and so this deal would have to be cut in front of the judge.
You can do this several ways. One is to hire a lawyer and have him with you to cut a deal in two days. The other would be to plead not guilty and ask the judge for a new date to come back with a lawyer (or to appoint you a public defender). With a lawyer you'd likely be able to work this out where you could avoid community service and then just leave.
Or you could plead not guilty, ask to hear what the DA's offer is and if you can get the violation or ACD, see if the judge would let you avoid community service. Then you could enter a plea of guilty immediately and get rid of the case without having to worry about the community service.
If not you can put the case over without taking the plea, and as long as you are back by your court date, you are free to go where you want in between. Generally there's a month's time between dates.