hello! i used to have the same problem when i shaved there too, and honestly the only two ways that prevent from those painful spots and ingrown hair is waxing, it's painful but worth it, plus it takes two weeks to two months to grow back! or laser hair removal,after about 10 sessions the results are great. but i'm afraid i can't help with getting rid of the spots now,i'm using the same alcohol thing and antibiotic cream and it helps a little.but seriously please stop shaving it'll only get worse hope i was of some use.
good luck!