It's not possible to determine exactly what your problem is but the closest approximation would be swelling of the outer layer of the eye (conjunctiva) and the swelling is causes "chemosis" You can Google Images chemosis of eye conjunctiva. It can be due to inflammation, irritation and also to contacts that are not fitting properly. You should have an optometrist or ophthalmologist that fit your contacts. I suggest you leave them out and go in to see him/her for a diagnosis.
I have it too. Is it possible to get rid of it? If so, how?
It's normal Re-read my answer
JCH MD
i have those too.. is it something serious and will it disappear overtime?
That tissue is normal. Its the conjunctiva. It gathers in folds at the inside of the eye and is called the plica semilunaris and the caruncle.
JCH III MD