I think you've largely answered your own question. You don't really need to say "insurance", as it's obvious from the question, but you could if you wanted to.

I see two possibilities. It depends on whether the request to the insurance company was made _before_ the medication was administered, or _after_ administration.

If the medication was not yet administered, it would be "prior authorization" (US) or "prior authorisation" (UK). You are requesting approval to use the medication.

If the medication has already been administered, then I think "request for reimbursement" would be appropriate.

In the samples below, I use the verb "make". The sentences could also be restructured to make "request" the verb, as in:

Prior authorization for XX was requested.
Reimbursement for XX was requested.