Can someone explain to me how come it's the white of my eye swelling?

The swelling of the: Outer lining of the eye (conjunctiva) is usually a sign of non-specific ocular surface irritation (e.g. Excess rubbing, allergies, etc.). The clear membrane (conjunctiva) covering the white portion of the eye is called the sclera. When the conjunctiva is swollen it gives the appearance you describe. The medical term for this is chemosis.