I think I have an allergy to eyelash glues. My eyes get itchy, sore, and swollen. What can I do?

Stop the glue. The glue is likely either creating direct irritation, or you are allergic to it. Either way you need to stop using it. Cool compresses may help reduce swelling and itching. If you want longer lashes, consider discussing Latisse (bimatoprost) with your eye doctor.
Stop using the glue. I know it seems obvious, but stop using the glue for a while. If the itching goes away, then try the glue again. If the itching comes back, then you have made your diagnosis, doctor!