How do i avoid razor bumps in the bikini and underarm areas?

wen i shave my bikini and underarm areas (especially bikini) i get real bad razor bumps and ive tried everything such as i use a bikini razor as much as possible and after shaving i put bikini after shave on it but then i read the bottle and it says not to put it on any irritated areas so i stopped using it an started using some ointment my dermatologist told me to use and it does keep the ares from giving me any discomfort but doing little for the actual bumps themselves. And i read online it helps to shave the hair in the direction the hair grows and that did help it from giving me discomfort but no matter how hard i try it leaves stubble, and i have to say all my most unwanted hair is VERY thick and i heard from my mom that it is because i have Italian blood in me and it is something I'm gunna have to live with till i am old enough for lazar hair removal. I would love to be able to wear a real bikini or regular swimsuit an not be embarred of my bikini area. i would also like to join the swim team wen i get back in school this august but this problem is keeping me from it. PLEASE help me!!! D=