Pain in the back of tounge by throat. Is that an allergic phenomenon?

Throat pain. Allegic reactions cause itching and swelling but rarely if ever cause pain. If this symptom continues, see and ENT doctor who can see this area clearly with rhinolaryngoscopy. A quick and painless office procedure.
Allergy unlikely. Pain is not a usual allergy symptom except with swelling (angioedema) in a confined space such as swelling that involves a joint. The tongue is very elastic so can expand quite a lot without pain. Also, swelling without associated itching is unlikely to be due to allergy. I would consult an ear, nose and throat specialist.