Get on to the dealer first, don’t go straight to insurance. I don’t know which car you have so don’t know if it’s still under warranty as you said it’s nearly four years old. If by chance it is still under warranty and the dealer finds a problem which would be covered by the warranty that may be responsible for the bad shaking then it may also cover the replacement of the wheels if the damage to them is a symptom of something else.
Worst case is they will say to contact your insurance. But better to try the dealer first as it may avoid any excess you need to pay.