Request to be placed on the volunteer list to be bumped. Inquire with the airline about the procedure. In a busy time like now, these flights may indeed be full or overbooked, and volunteers to be bumped may be nicely compensated. Let us know how this works out.
A better idea, if OP has a legitimate medical reason preventing OP from flying, is to call DL and inquire about a waiver. If that fails, wait till closer to departure and see whether any travel waivers are issued (unlikely for FLL, but possible for LGA if winter weather approaches). For now, the weather forecast has a 60% chance of rain on Monday, so I would not count on a winter weather waiver, but weather may change.
Flights are extremely unlikely to be oversold, particularly the Wednesday flight (even if they are full). Further, although the Delta website and/or airport kiosk will sometimes ask at check-in whether you are willing to be bumped in the event the flight is oversold, and if so, how much you are willing to accept, the final decision will not be made until shortly before departure once the gate agent has a firm idea of the load on the flight. You must be at the airport to be bumped off the flight, otherwise you are just a no-show and will receive nothing.
The first ticket it's from LGA to FLL on Monday Jan. 21 morning (~7:30am)
Monday is the 22nd. Confirm the date on your ticket is what you think it is.