DW used to get quite a lot of meds that required refrigeration and it was never a problem. In one case we got directly from the mfr and in the other cases mail order from nat'l chain pharmacies (both Walmart mail order and Walgreens mail order). They were always sent at no extra charge FedEx overnight morning deTRlivery. They always came in a sealed styrofoam chest of appropriate size for the meds plus a half dozen or so freezer packs. Never once did they miss a delivery. We just needed to know where we would be camping on the delivery day and call the office to get the correct address for Fed Ex delivery. We also advised the office of the delivery and that we'd be arriving that day and ask that they hold it in the office till we arrived and that no special handling on their part was needed (the meds will stay refrig for several days in their office). We always found people in the cg that wanted a free styrofoam chest and free ice packs and we usually had a couple to give away each month.
Labs were also easy. She had a very cooperative doctor so we designed a form on our computer for lab orders which he signed. When she needed labs, we'd just reprint the form, google "blood lab near us", put the address in the GPS and bring the form and ins. cards to the lab for blood draws. When the doc wanted different tests or add'l tests, we'd get an email about it and pull up the form, make the needed changes or adds and print. We used the same form off our computer for well over 10 yrs just changing the date every 6 mo or so. Never was an issue with the labs. We could also add special instructions like "provide a copy of the results to the patient" or have them send a copy to a second doctor.
Don't know how the botox shots would work by DW also periods where she got monthly infusions. At first they were done at a local hospital wherever we were and again her doctor would provide us via an email scan with the Rx. In later years, we found more and more private infusion centers and they were even easier to work with - they operate on a profit motive looking for as many customers as they can get through in a day. Not sure how that would work for you. I went for 3 yrs with shots in my eyeball every 3 months (after we stopped FTing) and I'm a bit squeamish about a needle going in my eyeball. Not sure I'd have that done at some profit motivated 'clinic'. Not sure if what you are talking about is an actual shot in the eye though.
Don't make FTing more of a problem than it is. Think of it as though you were just on a vacation and didn't want to drive 500 miles back home just to get your refrig meds. You'd call your pharmacy and tell them you're on vacation and need to have your meds shipped to you this month. They do it all the time. Then just 'rinse and repeat' every month, 3 mo or 6 months. No one needs to know that you're "homeless" :)