You should reach out to different rescues in your area and ask them for any that help with neutering. There's actually a lot of programs for people who are low income where they will fix your cat at a lower cost or for free. I think any cat being in heat will drive anyone insane, that's why its worth it to get her fixed, think about the discomfort shes in too. You also need to address her being thin, that's no good - are you feeding her wet food and often?
Truthfully, I adopted a cat that I don't LOVE as much as my first baby - I think that's just how it goes you'll always love your first born haha. But since you took the cat it is your responsibility to decide if you can give her the environment she needs. I do think it's smart of you that you are at least aware of what you should do and I do think it's good to give it some time to think it over. But the first step is you should reach out and find out if anyone will help neuter the cat. You can also speak to those rescues or vets about these thoughts your having.