How does your shop handle dental infections?

Curious for insight from y’all on how you handle dental infections?

I recently joined a tertiary care center without oral surgery support. We receive a fair number of transfers for dental infections. The patients are often not septic and without airway compromise. We often admit and give antibiotics but the surgeons here won’t intervene unless there’s airway compromise (ENT) since they aren’t oral surgery trained, so the patients just sit around on antibiotics. We don’t have OMFS on call but our competitor health system does. Is it reasonable to discharge stable patients with referral for outpatient oral surgery follow up? All of the local oral surgeons are private practice and either don’t take insurance or don’t take Medicaid.

Feeling kind of stuck on the right thing to do here. Appreciate any suggestions!