I’m sorry. I know US healthcare sucks. However, your best bet for healthy teeth is to brush and floss regularly, not to use unscientific home remedies.
If I wanted to whiten teeth at home -- I don't, but if I did -- I'd probably use those whitening strips, which it looks like use hydrogen peroxide.
Coconut oil is what movie theaters use on popcorn and IMHO is the best use for it if you've got some. I used to keep a jar of it along with some Flavacol to get the movie-theater experience.
EDIT: I later switched to a mix of chili oil and olive oil for popcorn, which is not as authentic but can be misted with a mister without congealing in the mister and is also pretty good.
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.
Curious why you would ask this here instead of just doing a web search? If you don't like reading search results, you can just get an AI summary. It's at least as reliable as asking a bunch of internet randos chiming in. Here you're probably more likely to get "10W-40, twice a day" answers over serious ones.
Personally, I prefer 5W and only oil pull once a month.
Because 95% of SE results are either paid in one way or another, or AI generated SE optimized crap mithout meaning.
When I want some actual opinions from real people, I always search "how to X lemmy" or "how to X reddit" (yes thats the only thing I still use reddit for, because it has so many more users)
Maybe spreading misinformation that unscientific home remedies are a substitute for modern dentistry, but that's a larger assumption than I wish to make of OP. I'll just go with good ol', "I forgot Google search exists".