I went through this recently and ended up calling the Montreal SPCA to see if they had a low cost spay/neuter program. They didn't but were able to give me a few phone numbers of people who did for about $40. The only problem was about a 2-3 week waiting time, but if you have to wait until she's out of heat anyways then this might be ok for you (and there might be less of a wait in Toronto anyways).
As for your question about the heat I'm not sure, I have also noticed cats in heat get more excited when you pet them. I have also noticed with some cats it helps to play with them to get their mind off it. Have you tried this? Or some extra yummy treats or catnip or something? I don't know if they are really in pain in the usual sense of the word, I kind of doubt it, I'm guessing it's more similar to a really strong hunger pain
but who knows! Good luck.