Question about a second loan?

My credit isnt that great, I took out a loan in june of last year for 4,000( augmentation) my ex husband co-signed with me, but its my name that is on the loan. Since the divorce, i have no vehicle. ive been borrowing my fathers piece of crap car which has broken down on me twice. I have a 14 month old and i cannot let that happen anymore. I only have about 500 dollars in my savings. Would my credit union let me take out another loan while i still have the other loan? Let me add that i have never been late on a payment, it comes right out of my check every 2 weeks. My credit union is through the hospital i work at. And now i would not have a co-signer... Would they even let me apply for another loan of 2-3 thousand to buy a used car? And since ive never been late on a payment would that help my chances of getting it alone? Any advice would help, thanks