Forced into medical leave

I've been employed with Amazon for a year and a month now. I've never had a really bad experience with my facility until today. I woke up feeling extremely sick and couldn't make it out of the house without throwing up at least twice. I felt so weak I wasn't sure I could drive. I couldn't miss work because I have no PTO and only a couple hours of UPT left. I made it to work and only lasted 2 hours. In those two hours I literally threw up at least 7 times. I constantly felt like I was going to pass out and my stomach was upset like crazy. The manager on the floor happened to walk by and ask me how I was doing. I told her what was wrong with me and she said oh we can walk you Amcare but I don't think they are open (it was 6AM). I told her then there's no point in going. I told her I couldn't stop throwing up and she basically told me not to go to the bathroom so much because I don't want to get a write up for time off task. Seriously? Did she even hear me? I can't stop throwing up and I feel like passing out and she's worried about time off task? I made it to my break just barely (7AM). I was standing in line to talk to HR to see if I had any options and the same manager from earlier comes to me and says she's walking me to Amcare. The Amcare "doctor" was a joke. He told me it sounds like I have the flu and there's nothing he can do, and if I have time I should just go home. I told him I didn't and he basically just told me to go to HR. The manager walks me to HR and I explain my situation. The girl basically tells me that since I don't have any UPT or PTO my only option is a medical leave. That I would have to call some number and open a case, see my doctor, and fill out all these documents. Otherwise if I don't I'll be held accountable for my time off work. I took the number and left the office and was basically forced to clock out by the manager. I went to my car and called the ERC number to set up the leave asap. The man who helped me on the phone by the way was so kind and helpful. I wanted to cry because I was so stressed out. Was I really in danger of getting fired for this? Because I'm sick, have no time, and would have possibly went negative on my hours? HR seriously couldn't have just hooked me up with VTO for the day? I'm beginning to think I should have just gave in and passed out in the middle of the facility. It would have probably been more effective than going to the people who were supposed to help me.