My belly button is red on the inside, there was a yellow-ish crust around it. Will Bactrim (sulfamethoxazole and trimethoprim) and neosporin help?

Maybe. It sounds like you might have a belly button infection. Bactrim DS: one pill twice daily for 10-14 days may effectively treat minor belly button skin infection as long there is no belly button ring present or it is removed. You may also have a more severe infection therefore you should see your primary care doctor for an examination and more detailed evaluation.
Maybe. IF belly button is red on the inside, there was a yellow-ish crust around it.See md get exam evaluation for infection.