I have a sulfa allergy and typically have a bad reaction anytime I use any antibiotic ointment. What would be the best for a slightly infected i?

Eye antibiotics. Other than sulfa, antibiotics for eye infection include erythromycin eye ointment and tobramycin eye drops. There should be no cross reaction with your sulfa allergy.
No antibiotic. If your question refers to an eye infection that appears mild, watchful observation only is required since most infections are viral and resolve spontaneously. If your symptoms appear to be recurrent a different etiology is to be determined. .