Any ideas on stopping my female cat constantly licking and scratching her fur?

My female cat constantly licks and scratches her fur. The fur on her tail is nearly bald and she has a lot of sores on her, so we are a bit reluctant to use a flea spray/powder. She sits on the edge of the bath, kitchen work top, tumble dryer, plastic bags and boxes. She runs like crazy over the lounge carpet to get to the window sill or sofa etc. We have sprayed the house with a strong flea killing spray and we always make sure that we hoover and keep the house clean. This is driving her crazy and we don't think that she is sleeping very well. She hates wearing flea collars, they end up being bitten off. Is anyone else experiencing the same problem or any suggestions would be gratefully appeciated.