Paid sick leave benefits for part time workers

I work at a restaurant in Fort Myers, Florida which is part of a huge restaurant group headquartered in California with over 200 locations in the U.S. We do multitasking like serving customers to lifting heavy pots with food from the cooks to the serving counter to cleaning the whole place. i was diagnosed with inflamed tendons on my left lower arm just above my wrist which I feel I got from my work at the restaurant. I was advised to rest it for 2 weeks at the very least. The acting manager said that I can take 2 weeks off after which I can decide if I want to come back and that I won't be paid for those weeks. I have been with the restaurant for a little over 2 years now and a former manager there told me that I should get at least 3 paid sick days. The acting manager admitted that it's the first time that she has encountered it and even said that she would refer it to a supervisor that comes around once in a while.