You're right to be being concerned about fit at your size, but are you finished growing? If not, your current bike will be fine for now if it's comfortable....and there are relatively inexpensive ways to make a bike more comfortable. I'm short and have been around and around with frame size because I have a short inseam to boot. I've had to scrutinize bike geometry in ways than an average-sized rider will never need to, but it has paid off.

Generally speaking (as in unless you get a lot of parts for free!), building a bike from scratch will be more expensive than buying a complete bike from a store (LBS, for example) or finding a used one on Craigslist, etc. If you decide you enjoy riding and want to stick with it, save up more and see what's out there. If you still have fit issues by then, you'll be glad you have more money to spend on a bike that fits you. Best of luck!