I currently charge $15 for walks and visits. I am thinking of raising my rates to $18 so that I can actually receive $15. Will this hurt me?

I think the best thing to do is look at the competition in your area and see what those sitters are charging for walks. Where I live (suburb west of Boston) I charge $20 so get $16 per walk and no one seems to think that is high. If you have a bunch of established clients who are happy with you, that $3 shouldn't make a big difference to them. Good luck with whatever you decide!