I have really bad allergies around this time, but lately my eyes are really red, today there was a huge red dot, can it be a burst vein?

Yes. A bright red spot over the white part of the eye (sclera) is probably a broken blood vessel. It should get better after a couple of weeks. As it goes away it may appear yellowish, which is the blood breaking down to hemoglobin. This would not require treatment.
Sub conjunctival i. You likely have a sub conjunctival hemorrhage these are usually self limited. Some doctors like to give antibiotic drops for this. You may want to ask your ophthalmologist for your allergies, most nasal sprays help with the eye symptoms bit some people need antihistamine eye drops. Good luck and good health!
Red eyes. Yes the spot can be a burst vein from rubbing your eyes, now why do you let yourself suffer like this, why don't you see an allergist?