I disagree completely with the need to get a 16hh+ horse to be competitive in dressage. I am just a bit larger than you (5'3, 110 lbs) and my 15hh horse is perfect for me. If you like larger horses, then go for it! Don't buy one just because you think it is necessary. Just as tall riders don't look right on short horses, a short rider doesn't look as well-matched on a short horse.
When I was looking for a dressage horse at the age of 15 and almost exactly your size the height range that I was considering was between 14.2 and 16hh. I did pass on looking at some light boned horses at the small end of the scale because my legs would come down too far, and I potentially had some growing to do. Anything larger than 16 and I just wasn't interested. If I were to do it again I might be less concerned by the upper size limit, but in dressage horses it seems that larger = pricier. Also consider the horse's gaits- if you get something smaller then make sure they don't have a teeny weeny pony trot as that isn't so conducive to successful dressage! Maybe for just having fun, but a good mover is a huge asset in a dressage test.
If I were you I would consider anything 14.2 and up, as well as the build of the horse. You're obviously not going to be too heavy for anything light boned, but your legs may come too low for that "perfect look" if it's short and fine. If the height is questionable then I would have someone with you take pictures while riding and standing so you can see the full picture for yourself. If you still have some growing left to do then don't push the lower limit, but don't pass on the perfect horse just because you think you need a giant to be competitive in dressage! I did alright on my 15hh horse when I was showing, and I love his height. I had a friend quite a few inches taller than me (probably 5'8+) who rode her 14.3 lightly build Morgan/Arab in schooling shows and did well. She did eventually upgrade to a new horse, but it didn't hurt her too much in the show ring!