Smooth23

Okay here's my question. Basically, I want to get financing for a car and I'll be looking at financing roughly $22,000- maybe as much as $24,000. I already tried to get financing through one dealer and they turned me down based on the short length of my credit history and because I only have one thing on my report- my current car, which I owe $5300 on (worth about $9500)
Here's my moola situation: I'm 21, I make about $32,000 a year. Credit score is 661 I have roughly $4,500 in savings, $75/mo cell bill, $195/mo orthodontics(2 years, zero interest), $250/mo insurance(im getting jipped i know), current car is $160/mo. Should I just pay off my car with my savings, and try to finance the whole amount of my new car- then sell my old car outright and put about $7000 into my new car and refinance for lower payments?(all this is assuming i could get my new car financed at all). I'm just trying to increase my odds of getting financed, really- I know I can afford it if I can find someone to work with me. Thanks.

edited cause I left out one of my bills.