A HEPA filter doesn't give you extra oxygen, it's more likely you've got allergens in your house. Clean up and vacuum the room thoroughly, change your sheets daily, at least for a while. You may also consider putting a filter over the A/C vent, sometimes crap can grow in the ductwork.
A fan will actually tend to stir up dust and allergens, but the white noise it makes can help you sleep.
You might want to spend the money to buy an air quality meter, if you don't have a friend you can borrow one from. You'll want to check for volatile organic compounds and carbon dioxide levels.
White noise is great, can attest to that. Drowns out noise or tinnitus. I've been sleeping with a fan turned away just for the white noise alone for three years now.
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