Perm?

Perms will make your hair appear a little shorter.  They are also very damaging, probably even a little more so than straightening your hair with heat every day. 

Some people's hair holds perms, other people's hair doesn't (they fall right out of mine and my relatives hair after a couple of days, making the damage not worth it).  Some people's hair holds them beautifully though.  There's no way to predict which you will be, (unless you want to curl one hidden piece and see how it goes with that strand for a few weeks first.)

Any chance you overlooked making the most of your natural waves?  It would certainly be the easiest and least damaging way to go.  Have you tried not combing your brushing your hair after you are done washing it?  Meaning never brushing or combing it when its dry.  Sometimes this can make wavy hair go a little curlier, and definitely reduces frizz.  You can also try oiling your hair.  Use just one or two drops of oil spread through your hair, only from the ears down (when it is still damp because you don't want to handle yours too much dry).  One or 2 drops won't look greasy at all, (if it does you used too much).  You can use jojoba, coconut, (or even olive if you have some at home and just want to try to see if you like it.)