The appearance of your eye is concerning. While we cannot make diagnosis over the internet that does not look like common allergy, not a broken blood vessel and could even be a non-malignant type of tumor of the conjunctiva.
You should make an effort to see an Eye MD ophthalmologist that specializes in "cornea and external disease" medical school ophthalmology faculty usually have these and with some effort you can find them in private practice.
This may need to be biopsied. Please take action. Let us know what you find out