Ok, I had a piccolo that was in storage for about 2 years, and I thought it worked, at a football game, i realized the G and Bb were stuck, my director didnt have oil, so he used 3 in 1 oil. It nearly killed me to watch.

It worked, and i was able to play, but did this somehow damage my piccolo?

3-in-1 oil is not ideal, but it shouldn't do any permanent harm. The real danger is applying too much oil so that it soaks into the pads. If that happens, the only real fix is have the pads replaced. It would be a good idea though to take it into a flute repair shop to get a clean, oil, and adjust (COA). If the keys were sticking, then there is probably old oil residue and the only way to properly take care of it is a COA. With a COA, all the keys are removed, the steel shafts are cleaned and re-oiled to prevent the problem from happening again. Also, it's checked for leaks and adjusted for good working order. If any pads are damaged, the repair tech can take care of those at the same time.

Around how much would that cost?

Depends upon the shop and how much extra work is needed. Generally starts around $50 for minimal work. Really good pro flute shops may charge $200 and up.