How to fix uneven eyes caused as an aftermath of a stye infection?

you have not posted photos, so it's very hard to know exactly what the asymmetry involves anatomically.  Without an exam, it will not be possible to fully evaluate you and give you recommendations. 

Without a photograph it is difficult to give a good answer. Typically a chalazia(stye) that drained on its own should not cause a Ptosis(droopy eyelid)of the eyelid but they can sometimes stretch the skin. I have seen a couple of patients that had styes drained by doctors where they went too high in the eyelid and accidentally cut the levator muscle causing a Ptosis of the eyelid.  You would need to be seen for a consultation to determine which condition you have but either one can repaired. 

Hard to say without pictures to help, but you may have an issue with the levator muscle that elevates the eyelid. Your upper lid should cross the upper iris revealing no white of the eye. If it is down close to the pupil, you will likely need to have the muscle repaired to fix this problem. Could be other things though. You should seek the advise of an oculoplastic surgeon.

A droopy lid is called blepharoptosis or simply ptosis. You may need a minor surgical procedure to correct this  condition. I would advise you to wait a few more months before pursuing treatment as it still  may return to a normal position. If indeed the droopiness is so minimal that only a friend noticed recently, it may not be worth surgical repair and it may have been there for much longer than you realize.

Hello and thanks for your question.  Based upon what you're describing, you likely have a droopy eyelid (aka: ptosis), making the eye appear "smaller" than the other eye.  A stye or infection of the upper eyelid can cause ptosis as a result of weakening of the eyelid muscle.  I would wait a bit longer, since the ptosis generally improves.  If it is still present in another 3 months, it can definitely be corrected with a ptosis procedure.  

Eyelid asymmetry as a result of treatment of a stye, the aging process, born with that appearance (congenital), as a result of trauma, or as a complication of previous surgery can all be addressed in some manner.
In most instances the asymmetry requires minor surgery, usually only addressing the skin instead of the orbital septum or wall of the eyelid or the fat pads. Some patients may have a rare issue with a droopy or ptotic lacrimal gland that produces the tears.
Sometimes a dermal filler to add volume to the area immediately below the lower eyelid fat herniation. Additionally, the skin of the lower eyelid area and much less needed to the upper eyelids, a skin resurfacing procedure can be performed to smooth the fine wrinkles and tighten excess skin.
The eyelid asymmetry procedure can be performed with local anesthesia alone, although some patients prefer some oral sedation. The good thing about the eyelid asymmetry, in almost all cases it can be improved or successfully addressed.