Oil pulling itself doesn’t benefit your oral health. What does is you taking a sudden interest in your oral hygiene, and rinsing very fucking thoroughly (often also brushing far more thoroughly too).
Cut sugars (even natural), cut acids (anything sour, tart, fizzy - yes even sugar free pop!), brush with as high a fluoride concentration toothpaste as you can (e.g., clinpro 5000 or neutrafluor/duraphat 5000), floss and use interdental brushes, don’t graze, manage your gastric reflux and dry mouth… Taking on board at least some of these will improve your oral health.
And for whitening, the whitening strips from crest/oral b work well if your teeth and gums are healthy and clean.
Arguably speaking, even new filament can be wet, so a filament dryer would be necessary regardless of what you do.