Broken and fractured are used interchangeably by many doctors. It depends on whether they are speaking doctorese or patientese. Like stitches or sutures, forceps or tweezers, idiopathic or of unknown cause at this point.
Minor buckle fractures of the bones of the forearm, if the bones are straight heal beautifully with a splint in kids, even better than with a cast!
A Randomized, Controlled Trial of Removable Splinting Versus Casting for Wrist Buckle Fractures in Children
Sadly there is a lack of quality data on the same question for adults.
Conservative interventions for treating distal radial fractures in adults - Cochrane Database of Systematic Reviews - Handoll - Wiley Online Library
If the injury is not the bones of the forearm but rather the small bones in the hand risk of poor healing even with good care is increased.
Edit: Unless you are in significant pain, an uncomplicated fracture should be able to be initially handled by your PCP or an Urgent Care with a referral to ortho if needed.