Hi Friedfish 
You sound like you're in a very similar place to I was a few months ago. I only saw my GP when a worried friend confronted me about her concerns and nagged me (in a nice way!) into making an appointment. So for a start, well done for taking the first step towards getting better and seeing your doc.
I was diagnosed with GAD and was also having panic attacks, so was really nervous about the 'increased anxiety' that can be an early side effect of the meds. But to be honest, I was feeling so crappy anyway, it was hard to tell if the meds actually made me worse, or if they just hadn't started making me feel better yet (if that makes sense!).
I basically told myself I had to accept I was going to feel a bit shitty for a couple of weeks once I started the sertraline, but that at the end of that time I would start to feel better. Look at it this way - if you don't take the meds, you will probably feel shitty for much longer than two weeks, without the 'light at the end of the tunnel' the meds will give you.
My advice would be to start on the meds and count down the next two weeks in your head, telling yourself that every day is a day closer to getting better. And be kind to yourself, get lots of rest, and sleep if you need to (tell people you have a virus if you need a cover story). And I don't know what dosage you've been prescribed, but I am on 50mg and took half a dose (breaking the tabs in half) for the first week, so the side effects weren't so bad.