1) People recently (within the last year) have been posting that they have been provided a refrigerator free of charge for medical reasons. Some of the hotels reportedly are providing those little shoebox size ones; some are providing bigger ones. Ask at the desk when you check in. Be sure to check your statement when you check out to see that you were not charged for it.
2) They had stopped providing refrigerators free of charge for a while. We had heard the same reason that tjmw2727 posted; too many people without medical needs were saying they needed a refrigerator. So, the choices people with medical needs were given were to pay for a frig or store it behind the desk like spicycat had to.
3) You might want to check with the Pharmacist to find out if refrigeration is required for the brand of Amoxicillin you have. Depending on the brand, it may not need refrigeration. Sometimes refrigeration is recommended to improve the taste. Sometimes it's to increase the safe storage time from 10 to 14 days. I'd still probably want to store it in a refrigerator if possible, but it's nice to know if you have any options.