The only way to apply for a new
TN is while
making an entry into the USA. So you can't just go to a POE in Florida, unless of course you fly/sail out of the country and then return through a POE. However, I'm assuming the POEs in Florida are not as familiar with the TN process as those on the Canadian border which means that while you can do it that way, it might be a little tougher dealing with an inexperienced goverment official. I would suggest either flying up to Canada and then applying as you go through US CBP at the airport or else drive over the border and apply at one of the land crossings when you enter the USA. If you were in the Western USA, you could also apply at a Mexican land border POE, but since you are in Florida I'm assuming the former options are better for you.