I don't know for certain if I had long covid but I experienced weird symptoms in my body beginning in January when there where >30,000 new cases per day in my country.
I was fatigued, had unexplainable chest pains some of the time, had problems concentrating, headaches, always a runny nose. I never did a antibody test because I self-isolated for most of the time and never met people without a mask, so I initially thought I was just developing an allergy. Multiple doctors tried to find out what was wrong but all tests where pointing to me being very healthy.
Then I got my second mRNA shot in July and all those symptoms went away, like magic. Very weird for me and maybe I had long covid and what you described happened.
While You’re the only one able to judge your personal experience and I can only go by what you have written, I have close Friends and relatives who had similar experiences. Runny nose in particular was not seen as a Covid Symptom in adults by health authorities at the time. Chest Pain is a common symptom of anxiety. All my Friends who had similar symptoms and got antibody tests prior to vaccination had no Covid antibodies. Let me suggest an alternative explanation that might or might not also apply in your case. Constant stress and anxiety about catching a horrific disease or loosing family members lowered the immune response as it is a well known effect of stress. Being fully vaccinated not only lifted that anxiety but also gave the immune system a boost. Thus no more infections with beta-coronaviruses and other viruses that caused the runny nose.
Immunity acquired through vaccination or natural infection helps prevent severe illness, which is likely to reduce the risk of damage to areas of the brain responsible for smell and taste [1][2].
AFAIK, there is currently no scientific evidence supporting the idea that mRNA vaccines uniquely "treat or cure long COVID" through other mechanisms.