NO, these straightening combs do not cost that much and no, it wouldn't take long at all to straighten your hair out.
comb This is one of the better combs
looks like same comb and you may find a better deal!
You actually roll the back of the comb to go against your hair section as you comb down to use the heat from this to smooth it out. It's as fast as slowly combing down each section would take...front right side, back right side, center, back left side, front left side at about 8-10 seconds each section.
I said I'd have to actually see your hair. Something tells me that if you let it grow out on top like Johhny Depp's and layer from just below the ears, that maybe the weight will help to straighten it up, especially if you get it cut (shaped up out of the the uneven ends it has now) that it may behave better and not be so bulky or wavy. So that would be a style similar right there.