One thing you're hung up on I think is medical-type definitions of "injury." Legally speaking (take the many standing cases we've seen in constitutional litigation), "injury" is synonymous with "damage." In civil cases, the injury is often monetary, only, such as in a breach of contract.
Take simple, common-law assault. The injury there is threatened "offensive touching." For battery, it's actual offensive touching. No medical injury required in either case.
The touching makes it "bodily," as opposed to "touching your stuff"/Francis, which is not actionable as assault or battery. But then statutes have come into play changing stuff around from the common law, renaming battery as assault with touching, etc.
The Texas Penal Code provides "Bodily injury" means physical pain, illness, or any impairment of physical condition. So it just has to hurt a little, beyond being merely offensive. It further provides "Serious bodily injury" means bodily injury that creates a substantial risk of death or that causes death, serious permanent disfigurement, or protracted loss or impairment of the function of any bodily member or organ."
So, earlier, when I said "requires medical treatment," that was probably a more common-law tort definition of serious bodily injury. But anything that requires medical attention very likely creates a substantial risk of . . . " Otherwise, why seek medical treatment? That doesn't mean you can go to a doctor for any old ouchie or hypochondriac condition and make it serious bodily injury, but the nature of most medical treatment is to avoid it becoming a bigger deal by infection, failure to heal, etc.