Is having post concussive syndrome something to worry about? My wife is upset since my daughter's doctor visit.

Tincture of time. Post concussive syndrome occurs in the weeks and months following a concussion or even a minor head injury. This is usually a constellation of headaches, memory problems and personality changes which are most often self limited and resolve just with passing time. This is not a major illness but can cause significant disruption of a person's life if symptoms are severe enough.
Maybe. No one knows the long-term effects of a single concussion. If managed appropriately, with both physical and cognitive rest, your daughter should recover well. The most dangerous complication is a second concussion or brain injury before she has fully healed. This is the reason to stay away from contact sports until she is symptom-free and cleared by a neurologist to return to play.