The laws could differ from State to State and city to city or towns and you'd be better off asking someone in your local area about the laws.
But I don't think it would be illegal to go in public in just a diaper and shirt since you'd be covered up and not showing your private parts but I would advise against it as even though it may be legal it's still indecent and nobody wants to see an adult wearing nothing but a diaper.
I don't even like seeing babies or toddlers in public wearing nothing but a diaper and I think they should even have their diapers covered up in public.
You can do what you want but I would advise against wearing just a diaper in public out of respect for the public.