Since the pain started after the scooter handle directly hit his chest and increases while getting up, turning in bed or laughing, it is most likely a chest wall/rib injury. It is a good sign that the pain has already reduced by 60–70% in 3 days. However, a small rib fracture can also present like this and there may not always be visible swelling.
Next Steps
I would suggest getting him examined once and doing a chest/rib X-ray if there is localized tenderness over the injured area. Until then, continue the prescribed pain medication, avoid heavy lifting and strenuous activity, and give the injury some time to heal.
Health Tips
Ice packs are fine during the first few days. Ask him to take normal deep breaths periodically and not tightly bandage the chest. If he develops breathing difficulty, increasing chest pain, dizziness/fainting, coughing blood, or worsening weakness, get him evaluated urgently.