I went through the same thing on the same bike in another thread "great knees of fire". Definitely be careful, knee pain is the worst. It took me 4 months to get back to almost normal, and mine still bother me on occasion. Its probably more fit that gearing, though bad fit, and a high gear will mess you up faster.
My problem was the clips and straps. I walk duck footed and having my feet strapped straight to the peddles was causing my knees to twist as I put pressure on them. A few months of that and it was hard to walk up stairs. I went with clipless egg-beaters, and immediately noticed a difference, though it took months for things to clear up completely.
I'm sure if you're having trouble affording a new cog, that new peddles aren't in your immediate future either, but check out your feet when you stand. If your toes point out or in it could be your problem. Get some peddles with some float and see.