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A whitish pimple like lesion can be seen at the junction of the white of the eye and the black part of the eye and is called a pinguecula. A pinguecula
is a kind of conjunctival degeneration( conjunctiva is the white part of the eye) and is a harmless condition. In the absence of pain or redness it does not require any treatment but for lubricating eye drops for soothening effect.
As you have mentioned reddish part of the eye, I got a bit confused, but I guess you meant the junction of the white and the black part of the eye, on the side closer to the nose. You can follow this link just to get a fair idea as to how a pinguecula looks like and check out if your eye shows a similar lesion.
If the pimple like lesion is seen in the innermost corner of the eye where there is reddish corner then it is likely to be the caruncle( normal anatomy). Sometimes the caruncle can get inflammed( but is painful) or even be slightly be larger normallyor develpo an abscess again a painful lesion or develop a lipoma rarely. I believe you can observe it as of now for any change in its size/color/occurance of pain, any of which if present requires a detailed eye check up.
Please feel free to ask follow up questions( if any).
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A bonus and positive feedback are welcome.Views expressed are for information purpose only and cannot substitute a visit to an ophthalmologist