Is using my sick time going to burn bridges?

I resigned almost 60 days ago due to the stress getting to be too severe I needed to leave for my health. My district requires 60 days of notice so after resigning I had about two months where I needed to stay. I have used a lot of sick time since I have resigned honestly just to get through these last two months, I also was super ill from the stress at one point. I have about six more days until im free but I wanted to take one more sick day to get a TB test for my new job. I am feeling guilty and like my current school will never give me a good reference even though I know I should use my days as we are not paid for the ones we don’t use. I tried to leave on day 58 but they are holding me to exactly 60 days. My admin has treated me poorly as a result of using my sick time and im afraid one more day will make it so I can never get a good reference in the future if I need it.