If she has had this problem the majority of her life, then it is not contagious to you or any one else. You would have had symptoms of similar issues by now if it was. The only skin conditions that are contagious from one species to another is ring worm and Sarcoptic mange. This really doesn't sound like either.
I would get her a skin scraping done to help identify what the problem is. She may be allergic to fleas, and putting her on good monthly treatment of frontline or Revolution can help resolve it if the the case. When a cat is allergic to fleas, it only takes one bite from one flea to cause a nasty skin reaction that can last weeks.
Another common problem many cats have that can cause similar skin and coat issue are food allergies. Using foods that are very natural in ingredients like California Naturals or prescription foods like Science Diet Z/D can help tremendously with food allergies and related skin problems.
There is no harm in putting neosporin in the area if you like. But I doubt it will do little good until the root cause is discovered. So I'd make that appointment. Probably a very simple treatment like new food or good flea protection is all that is needed to help fix this.