Last time I went to the clinic, they wanted me to make an appointment for 2 weeks later...

I'm actually sick though, so do you think they would just do a walk in?

I don't know if they'd do a walk in but I'm sure you'd be able to get an appointment for the next couple of days. I went in December, usually a pretty busy time, and was able to get an appointment for the next day easily.

They used to have a walk-in session, but I think they cancelled it. Your best bet is to go in early (at 8:30 when they open) and ask if there were any cancellations for today.