Two days in a row I've used ivory soap while staying at my parent's house. I cleaned the vaginal area twice each time as I was coming to the end of my period and wanted to feel "especially" clean down there! My vagina for days after felt like it had a low grade burning feeling. Could this be a reaction to the Ivory Soap or could it be an STD?

Yes it could be the ivory soap if you are being very diligent cleaning in that area. Very tender skin there and should only be cleaned with a cloth and plain water, or you can buy a product called Vagisil which is especially formulated for cleaning the vaginal area but you should not rub hard inside.

Last time I had a sensation like that, it was connected to a urinary tract infection and the burning comes along with it and aggravated with cleaning.

An STD, possibly if you have reason to think so.