I wouldn't go as far as to drastically cut your hair!
Why not try a product that can help with hair growth. There is this new one that I recently got introduced to that has been getting a lot of raves off of another hair board. Here's the link:
"Boundless Tresses Growth Serum"
Products in my current regime: Nioxin Scalp Therapy Shampoo, ORS Replenishing Pak, Curls Whipped Cream, Curls Souffle, Curls Spiral Curls Cream, Curls Milkshake, Curls Quenched, BB(Bonner Brothers) Growth Lotion