From my limited understanding of vitamins and minerals, sensitivities like these, usually indicated either too much or too little of the antagonistic vitamins/minerals related to that nutrient.
I have been 'allergic' to vitamin C for for years, it would break my face out with the most painful, sometimes itchy bumps. Turns out, my actual problem was low zinc and copper, as well as stored iron(borderline deficiency). When I upped my zinc and copper, and added molybdenum to help move my iron out of liver storage, my reactions to vitamin C-rich foods and drinks subsided immensely.
By the way, vitamin C naturally interferes with the absorption of both zinc and copper, and it is used in conjunction with iron in many bodily processes. Unfortunately, the body tries to keep upping the processes when it has one of the necessary nutrients, even if one of more of the nutrients needed are too low. This causes a wave of reactions all over the body, as the body attempts to meet the demands of a needy metabolic system. Eventually the system shuts down, but not before some undefined feedback system kicks in, and aggravating physical systems are manifested.
To locate the cause of the vitamin A sensitivity, look at your zinc and iron levels and your copper. Zinc moves vitamin A out of the liver. So high zinc could be moving more vitamin A than you either need or can actually use. Copper and zinc conflict with/balance each other, so a low copper level could affect zinc. Of course, a high copper level could have an effect also, if it has become biounavailable. Iron, works with vitamin A in several metabolic functions, so low iron could leave vitamin A with nothing to do but wreak havoc. Same goes for vitamin D.