How can I cure red, itchy, swollen, slightly bumpy eyelids/area around eye?

Eyedrops. Check to see if you are using a new skin product, as this can cause a reaction like this. If this has just popped up spontaneously, you can try using artificial tears 4x/day in both eyes. If that doesn't work, there is a OTC drop: 'Zatidor', which works well. You can also use Benadryl, (diphenhydramine) but this will cause drowsiness. If these therapies do not work, consider seeing an eye doctor.