There's nothing about OP that will worsen tooth infections. They'll worsen all by themselves if they're not taken care of - and fast. I've used a few drops of oregano oil and swished with Colloidal Silver in the past to get rid of tooth infections.

Coconut oil does whiten teeth - it could be that sunflower oil yellows them like olive oil and others, but I've never tried it.

How fast you see improvement with OP will depend on what the condition is of your oral health now, how healthy you're eating, otherwise taking care of your teeth etc.

In other words OP will improve your gums and general oral health if you keep it up - just make sure you're not taking 2 steps back with diet, hygiene, etc.