I would call your hair 'fine' From what you say, it sounds like you have alot of little tiny hairs.
The length will cause your hair to be flat. Fine hair is not strong enough to support the weight. To be honest, even if you had coarse hair (not tiny but fat) it would likely be flat.
Fine hair may even lay flat on top with a perm and would definately go flat again as soon as the perm grew out about one or two months.
The only thing I can suggest is to use a gel designed for fine hair. Apply it to the root area - right at your scalp - and blow your hair dry upside down, making sure the root area gets dry first, to give it some lift.
You could layer your hair so that the hair on top is not as long but that may thin out the ends, depending on how much hair you have.
