I'm going to assume that you have not yet had an initial hearing for the eviction. The first hearing on an eviction is the possession hearing where the landlord will state what reasons he or she has for evicting and the judge will most likely grant the possession of the property. At that point the judge should set a time frame for the property to be vacated. This is simply the landlord's right for not having been paid rent, so it will be fairly soon. Then there is a second stage of the eviction process where a damages hearing will be set sometime in the future to determine how much money is owed under the lease and the efforts of the landlord to re-rent.
Best of luck!
Mr. Coe is correct - the first hearing will be an eviction or immediate possession hearing. The second hearing will be to determine the amount of money the landlord is entitled to recover from you, if anything.
If you are behind on your rent, the Judge will award possession to the landlord. However, as for the date of possession - if you do not show up for the hearing it will likely be the day of the hearing. If you are present for the hearing, the landlord's attorney (if they have one) will likely try to talk to you before the hearing to try and set a date for you to move out. If you cannot come to an agreement or the landlord does not have an attorney and they (and/or their attorney) refuse to speak to you, the Judge will set a date for you to be out by. The Judge has some discretion and can give you anywhere from no time to 30 days - however both ends of that spectrum are highly unlikely. A typical time frame is 7-10 days. Depending on your medical issue(s), you may be given a little more time, but typically not much.
If you can, reach out to your landlord and try and working something out in terms of a payment plan to get caught up and do not fall behind on that plan. Best of luck.
While I appreciate the opportunity to answer your question, my thoughts and impressions of your case may change given more information. Typically, I would give advice following a face-to-face meeting where we could both ask questions of each other about your situation. Therefore, my answer is intended to be general guidance and not legal advise for you to rely on in your particular situation. Moreover, my response to you is not intended to establish an attorney-client relationship. If you would like to hire me as an attorney, you must contact my office and we must enter into an agreement for me to represent you.