Hello and hope you are doing well.
As there is tenderness, it could be an infection which is causing the asymmetrical enlargement of the tonsil. Sometimes persistent enlargement of the tonsil can sometimes be due to a lymphoma. It would be worthwhile to see if other lymph groups are enlarged namely, axilla and groin, these can be palpated, the others like those in the chest or abdomen may need a CT to detect their enlargement. Sometimes the tonsil may be removed for histopathological study. If it persists, you will need to consult your primary care physician for further evaluation, who may then refer you to an ENT specialist.
Hope this helped and do keep us posted.
The swollen gums is of concern. Oral health is very important. Are you brushing your teeth with an extra soft toothbrush 3 times a day? Have you tried different toothpastes? Are you flossing a few times a week? Have you seen a dentist in the last 6 months?
I would worry less about the tonsil and neck and more about your gums.