Can you be allergic to vaseline? I put it on my lips last night and now my mouth is swollen!

Not plain Vaseline. Plain vaseline is inert with respect to the immune system so will not cause any skin reaction. If it was flavored or had other additives, they rarely can cause a reaction. Most likely the swollen lips are unrelated to the vaseline.
Possibly. If you used pure vaseline and not a vaseline product that contained sunscreen, fragrance, or other chemicals, then it is less likely to have been an allergic reaction. After the current reaction has subsided, you can test this product by placing a tiny amount on a very small test site of your lip, if irritation develops a second time, then you have confirmed "contact allergy".