Seborrheic dermatitis is hard to get rid of completely, but episodes are treatable. A wide variety of shampoos and lotions are available, many of which are available over the counter. Although you didn't mention any scalp involvement, that's a common site. Shampoos containing tar, zinc pyrithione or selenium can be used daily. Shampoos containing the antifungal drug ketoconazole are used twice weekly.
Selenium sulfide is used once a week for the toughest cases.
Even if you have little or no scalp involvement, you may want to try using these shampoos. Treatment of the scalp is thought to decrease facial involvement. As you know, cortisone creams or lotions are also available to be used as necessary. If the topical steroids aren't working, you may want to ask your doctor about adding topical ketoconazole. You are right to be concerned about getting cortisone in your eyes.