So sorry to hear about the anxiety this neighbour is causing you. I can imagine how unnerving this must be to think you are being watched all the time.
Just throwing an idea out there. Has this other neighbour got a history of making odd accusations about other neighbours? From experience, an elderly family member, had a habit of accusing people of drug dealing, burgularies, kidnappings and even troups of clowns dancing down the road. She did actually see this happening in her head but clearly nobody else did. It could be something similar with your neighbour that her mind is affected by age/disease. Perhaps having a discreet word with any family members that visit her to express your concerns may result in her getting the meds or any extra care she needs. It is probably just be a coincidence that she has hit the nail on the head of "entertaining gentlemen". She may also be acting perfectly normally (or only a little bizarre) in front of family and friends but has moments of weird behaviour with others which will only get worse.
I know easier said than done but I would ignore her as you don't advertise there is nothing she can find out about you merely having family members, friends, work colleagues visit you and they just happen to be men. It is a massive jump to assume that those few visitors a week would be clients of a sex worker. Someone would have to actually be in the room as you have a booking to know for sure.
If you don't have blackout curtains just be careful about turning the bedroom lights on when you have a client round. I tend to keep the bedroom light on most of the time so it doesn't just go on just before or when a client arrives.
I wouldn't bother advertising another non-existant business as you will likely have a clause in your tenancy preventing you from working from home so that could cause a different set of problems for you and really not worth the hassle.
Hope it all settles down for you.
xx