There are several possibilities that could cause this symptom of sore throat/congestion in the mornings.
One possibility, as you mention, is allergies. Two forms of allergy can cause this, allergic rhinitis (nasal allergies) and sinus trouble. Both cause mucus to drip down the back of the throat chronically. This is especially noticeable at night, and may cause you to have night time cough or to wake up with a sore, congested throat. Other symptoms would include stuffy nose or sinus pressure and headache
Another possibility would be gastroesophageal reflux disease, or heartburn. With heartburn, acid from the stomach washes out of the stomach into the esophagus. When you lay flat, this acid may reach all the way up the the throat causing irritation of the lining of the throat. Other symptoms might include a burning sensation after eating certain foods and a sour taste in the mouth upon awakening.
All three of these conditions are very common medical problems and they are not usually serious. However, it would be good to know which you have, and a physical examination by your primary care doctor
should be able to sort it out. There are numerous excellent medications that your doctor can prescribe to help with these problems as well.