Is there any way other than hoemonal drugs that can speed up hair growth?

Sort of: I dont think you can speed hair growth without hormonal drugs, but you can improve hair growth with topical Minoxidil (rogaine) without prescription. The drawback is it only works as long as you use it.

Minoxidil: I agree - Minoxidil 2% in women, 5% in men 2x/day will help thicken the hair. Your length is almost predetermined by your genetics and how long your anagen (growth) phase is. I will sometimes recommend b vitamins 2x/day or l-lysine which may help, no huge studies supporting their evidence but some anectodal reports. Also, might have your dr check thyroid status and ferritin (iron stores).