Impossible. You had a burn from the liquid nitrogen which can happen. It is impossible to be allergic to nitrogen. Nitrogen is the predominant element in air so if you were truly allergic, you'd be long dead by now. Scientifically, you can only develop allergies to protein molecules which are organic compounds. Nitrogen is inorganic.
Burn not allergy. If you contacted this, you have a burn, not an allergy. It is super cold and "burned the skin". Inflammation occurs which is increased blood flow to the area to promote healing. Anti-inflammation medicines like Motrin or advil (ibuprofen) and protective dressings changed every other day or good skincream applied daily will help. If it blisters, keep them covered and protect the area until healed.
Burn. This is treated like a burn not an allergic reaction, speak to your treating physician for additional admvice.