From the symptoms you have described it looks probably due to a sty. It is also known as Hordeolum that is due to the infection of the glands or the hair follicle. Since you had been applying petroleum jelly on the eyelashes it may have led to the infection. This is quite common. Generally there are two types of hordeolum namely external Hordeolum and internal Hordeolum.
External Hordeolum occurs due to the infection of the hair follicle while internal Hordeolum is an infection of the meibomian gland that secretes an oily substance that lubricates the eye. The causative organism is staphylococcus aureus. The patients usually present with redness, itching, watering of the eye, and swelling which appears on the eyelid. Sty's are filled with pus caused by the infection. Usually it resolves in a week or so and doesn't cause any damage to the eye.
I would recommend a few home remedies that can reduce the swelling and ease your pain.
a) Application of warm compression over the swelling for 10-15 mins for four times a day. This will bring down the swelling.
b) Don't try to pinch or squeeze the sty as it may rupture and cause the spread of the infection.
c) Avoid the use of contact lens, eye make up till the infection is completely resolved.
d) Do not rub your eyes or apply petroleum jelly to the eyelids.
e) You can also use antibiotics or steroidal cream to reduce the swelling and painkillers like ibuprofen to relieve the pain.
f) If there is no relief, then you can get the sty drained.
However this can be done only in consultation with your doctor. I would suggest you to try this for a week and then reassess the situation after a week. Hope this helps.