These bumps that you are experiencing are called milia. They are essentially cysts with a skin-type substance inside of them. They are most frequently seen in infants, but certainly can be seen in adults. They can also have a fairly quick onset like they did in you. Generally, they will come and go, but otherwise do not amount to much significance other than local irritation and itching.
I would recommend using an over-the-counter 1% hydrocortisone ointment on the itching areas twice daily for a week or so or until the irritation resolves.
Do you have any other specific questions about them that I can address? Does this information help address your concerns? Does this make sense? Do you have any other concerns that I haven't addressed?
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My opinion is solely informative and does not constitute a formal medical opinion or recommendation. For a formal medical opinion and/or recommendation you must see an eye doctor.