First off, if you’re in dire need of a car and have poor or limited credit, you may have to bite the bullet for a little while. Building credit can take months. In the meantime, you may want to consider public transit (if possible), ride-share services, or a car you and your mother can afford with cash.
As for improving your credit, you can start right now. Many banks and credit unions offer low-balance credit cards, savings-secured loans, and other products specifically designed to build credit. Make sure to pay these off in full to avoid interest and don’t miss any payments. With any luck, you’ll be able to afford the vehicle you originally had your eye on.