Don't let anyone tease you into thinking a particular bow isn't a bow ( well, 'cept a crossbow).
Bows are tools, designed to do something. If you need a 1/4" nut turned, you don't grab a 1/2" wrench, and if you grab an adjustable wrench, you get something that does OK at a lot of things, but not really great at anything.
If you are 5'6" tall, you will by default have a smaller draw than a much taller person. Getting the most out of that shorter draw needs a bow that is made FOR that smaller draw.
Sounds like a shorter bow, be it "long" or "recurved" might just be the tool that works its best for you. An established and accomplished bowyer can make a bow that works in your parameters.
Give one a try and report back on how it works.
ChuckC