How to improve credit score within 2-3 months?

It’s time for a new car before the one I’m currently driving dies on me. I don’t use credit, I have no open accounts. There are at least 7 accounts in collections, in total about $2,500 unpaid.

If I paid these off, opened a secured credit card and started using it & paying it off every month, would I be able to raise my credit score enough to get at least 20% interest on a car instead of 25%? Preferrably higher, but I know I may need a year or two at least to create some history.

What do you think? Anyone with experience in this? Any advice out there for me?