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you may have leaned up against a table which had oil on it and it got on your shirt and bra without you knowing that you were leaning on a table with oil on it
this is more likely that your breast or body producing oil.
this oil would not be related to allergies in your eyes.
you may benefit from using over the counter allergy eye drops.
if your skin is very oily, sweat and oils on a hot day could have soaked your bra and shirt.
you may need blood test to check your thyroid hormone levels. hyperthyroidism can increase your metabolism and cause you to sweat more.
I take it you are not having any nipple discharge or breast discharge when you squeeze your breast.