Hello and hope you are doing well.
Persistent one sided 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. 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.
G'day mate :) I also live in Australia.
The lump in your gum could be a silavary gland that is blocked, abscess. I would suggest you see a Dentist about this as it is in your gums and he would tell you if you need to get further tests done on it.
It is good that you keep track of things in your body as you should be your own Advocate and you'll know best when something in your body changes and appear.
All the best and let us know how you are doing and what the lump turned out to be.