Hi,
How are you? A concussion may result when the head is hit, such as in your case, with a bat. The force of the bat may have been strong enough that it manifested at the opposite side. Full recovery is expected from an uncomplicated concussion. But symptoms such as prolonged dizziness, memory loss, decreased mental functioning, irritability, and headaches may occur. If cold compress or over-the-counter pain medications do not help, have this checked by your doctor for proper management. Take care and best regards.
I would definitely go to the doctor if it's been around 3 weeks. The worst that can happen is they tell you that you're worried about nothing, but I would be concerned that you might have damaged something on the right side when it moved that way when you were hit.