I visited Tampa some few years back and liked it... it reminded me a lot of Jacksonville... only nicer weather.
We moved down "recently" from Maryland so you are more than welcomed to come to me with your frustrations with the move.
I will tell you this... Im not sure about your insurance and whatnot but if Medicaid will be your primary insurance(for your child), it will take some getting used to what you are allotted every month... although we changed to a different plan in Medicaid(CMS) so that may or may not allow for more supplies. I doubt it. We have it primary and only for my daughter, which sucks. Also, I don't know if this is state-wide but apply or look into CMS(Children's Medical Services). I still have no idea how it helps, but apparently it's good to be in.
Since I'm from Jax I can't help you with docs but I wish you the best. As far as peds goes.. check and DOUBLE check the doctor will see your child. I don't think yours is on a vent but ours is, so that was very different to find a doc comfortable enough to take on a patient like our child. So just do some research and call the doctor's office NOW and explain to them your moving and if they would see your child and make sure they understand EVERYTHING you child has....
What I did with docs and specialists was quite simple.. go on your insurance website and find providers that are in-networks and called to see what it took to have your child seen.... ALSO, try calling the social worker at the children's hospital you'll be sending your child to if anything happens and see if they can help you with references to doctors and insurance stuff.
That's all I can think of right now... if I remember more stuff I'll be sure to add on