If im medically retired, is it possible to claim other injuries through the VA after?

While you are separating and receiving your rating, the VA should give you your rating too. If you have unclaimed issues, get seen about them now.

If the condition is service related then the VA will be responsible for all treatment stemming from the condition. The rating is all about disability pay you will get for the same condition.

Yes take your medical records to VA I was med sep for a back injury and VA rated me for that plus asthma and hearing loss I am currently rated at 100 percent