Also, in addition to the above, you should get a thyroid test done and get the kidneys checked. These conditions can manifest as skin problems. When a cat is 7 yrs and up, you should keep an eye on those conditions, as well as diabetes.
Good luck to ya!!
You should take your cat to a vet if you possibly can. This kind of condition is not uncommon and is likely an allergy - it can also be aggravated by anxiety, if your cat is the anxious type.
The vet will probably prescribe a steroidal anti-inflammatory along with a skin cream. There may or may not be a fungal infection involved, like ring worm. If so, that is pretty easy to knock out, but with the rest of the symptoms, you really need a vet's diagnosis and prescription.
Good luck! Let us know what happens.