I just found out, 10 days before I leave, that I have to have a small surgery on friday. I will still be in a bit of pain and recovering. Has anyone ever upgraded to first class on Delta at check in? Will it cost an arm and a leg? Our seats are toward the back of the plane and I am afraid this will be difficult for me.

I can not change seats as it looks like a sold out flight. There is nothing available to change to expect first class.
Just because the seat map for your flight shows that all economy seats are assigned does not mean that the flight is sold out.
There are seats in the forward part of the economy cabin that can only be pre-assigned to Delta's elite frequent fliers. Especially on leisure routes, such as to Orlando, these seats often often have nobody assigned to them, but they show has unavailable to "mere mortals." They are no better in terms of width or legroom than the economy seats in the back of the plane, but they're more desirable because you get off the plane more quickly. (Also, on rear-engine aircraft, they're quieter.)
On the day of the flight, the seats are under airport control and are assigned to any economy cabin passenger, regardless of frequent flyer status.
Other airlines, including United and American, do the same thing. On United, the seats in the forward part of the economy cabin have extra legroom and are called Economy Plus.
Start checking the seat map 72 hours before your flight. Chances are, however, that your best bet is to get the airport early to get a better seat assignment then.
I wouldn't count on first class, but that's a possibility. It probably won't be cheap. Moving forward in economy should be possible for no charge.