Florida Non-Compete

I signed a comprehensive non-compete agreement with company XXX in FL when XXX acquired a company I was working for. XXX is in the field of higher education administration software and I worked there for their services group. I had a medical emergency in Feb and was made to travel even after that for several weeks in a row which caused me undue hardship and forced me to resign. I took up a job at an existing client YYY in state of VA (working from home in FL). I recently received a letter from XXX asking me to resign or else face potential litigation citing the non-compete clause. The non-compete clause prohibits me for 12 months from working for any existing/former/potential client in any geography they do business in and they have over a thousand such clients, apart from working for any company that does business in higher education software. I believe this infringes on my right to work and virtually gaurantees me unemployment as this is the field I have worked on for the past several years. Would this stand a chance in court if I we go to litigation. They haven't filed yet, but have already sent me a letter indicating they might be doing so in a day or so.