Will shaving my head make hair grow back in bald spots?

I've had one or two bald spots and a thinning hair spot around my hair line but only from the front but they were not brought on by genetics, age or anything. We don't have hair loss in the family. My hair loss problem was brought on by straight perms, so that would be the heat damage of a flat hair iron and chemical damage from the straight perm chemicals. They're very hard to see but you could see them from up close. I've been trying to use natural treatments that don't involve using drugs. I've been more than likely using oils or hair growth vitamins that you'd find for Biotin. But I can't afford doing laser hair regrowth therapy because them helmets made for that are too expensive for me. So I was thinking, what if I shaved my entire head bald? If I shaved my entire head bald, would my hair regrow back in the parts of my head and scalp that are lacking? I've shaved my head before and my hair always grew back. But I never shaved my hair when my hair loss problem started. But I wanted to know, if I am to shave my whole head bald, will my hair grow back in the parts of my head and scalp that are lacking and showing signs of hair loss? I'd like to have as much of a reliable answer as possible before I do anything. The times I did shave my head was with an electric razor by a barber. So tell me, will shaving my whole head bald work in growing my hair back in the spots that are lacking and showing signs of hair loss?