Is hydrocortisone safe to use around my eyes and on my eyelids?

Sometimes. Hydrocortisone is a potent steriod that is available over the counter. It can be used around the eyelids for short periods of time but care must be taken not to get any in the eye. If used to long it can cause thinning of the skin. If used for more than a few days and the problem does not resolve, you should consult an ophthalmologist or dermatologist.