Jen,
Welcome to the site.
At a full stop, pull the shifter back to the 2 position. Then drive normally to about 45mph. If the car shifts once, then you do have first and second gear. Our transmissions will shift to 2nd at about the 10-25 mph area based on how much you press the gas, less pressing means it'll shift sooner.
The car running poorly can make it shift funny, however it won't keep the car from using first gear. A throttle body cleaning and tune up sound like they are in order if you decide to keep the car.
