Do not worry and just relax first. Avoid using your finger nails on your contact lenses since it can bring a tiny, unseen scratch or tear in the lenses, which may severely irritate your eye. While try putting the lenses into your palm carefully can you can put a few drops of cleanser onto it and then clean it. Actually you can use waterproof mascara.
If you do the mascara on the contact lenses, you could just take the contact lenses out of the eyes. Then you could use the solution to clean the contact lenses. This way is the best way to remove the mascara. Then you could wear the contact lenses again in the eyes. You should not leave things on the surface of contact lenses when you wear them which may let you feel uncomfortable.