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It is unlikely to be an eye infection .
The tiny white pimples along the upper and lower eyelsh margin are likely to be blocked meibomian glands. These are modified sebaceous glands present in the lids. These can get inflammed and cause pain.
You are already taking the correct treatment in the form of warm compresses thrice a day and baby shampoo lid scrubs.
Continue the same for 3 to 4 weeks. You can also use lubricating eye drops such as Refresh tears eye drops, 1 drop 4 times a day.
Look out for increase in redness in the eye excessive discharge. If seen then do get the eye examined by an ophthalmologist for a closer look and start of antibiotic eye drops.
If you need more help, please use the reply tab to continue our conversation. If you do not require further assistance, kindly rate my service.Thank you and best wishes.It was a pleasure to have answered this question.Views expressed are for information purpose only and cannot substitute a visit to an ophthalmologist