I used to have a similar problem. been a heavy binge drinker for over 10 years. also have a deviated septum and issues with post nasal drip. It sounds funny and weird, but if you have ever been to an AA meeting or know anything about the program, they refer to drinking as an allergy. I always found that I had lots of mucus production after drinking. its probably a response to the trauma drinking causes to the body, It does wear down the throat and cause irritation in the esophagus as well as the stomach. Ive found that an increase in the amount of acid produced in my stomach after drinking exasperated the problem and my sore throats worse. I wouldnt per say its coming from Covid or anything, its more of a concoction of everything all at once. Drinking also suppresses the immune system and when its back up and running you can go through some situations like these when its trying to fix itself. Dehydration plays a key into this, even if you are producing lots of mucus. Best bet is to cut down on the drinking, most of that will clear up after. also just know any time that you heavily drink again in the future after stopping or cutting back will result in the same symptoms again. So to recap, drinking wears down the esophagus and increases acid production, increased acid production can lead to the body making more mucus to protect you and keep the acid from spilling out the esophagus into airways and mouth. Increased mucus production will lead to more post nasal drip, thus causing the sore throat. Start drinking again, and the cycle continues. Headache is caused from the dehydration from drinking and over production of mucus. Hoped this helped!!
P.s. warm/hot tea or water with honey and lemon helps. Steam will be your best friend for a speedy recovery