Flight Crew Air Transport Pilot (ATP)
Flight Crew Last 90 Days 65; Flight Crew Total 14500; Flight Crew Type 7000
Aircraft Equipment Problem Critical; Flight Deck / Cabin / Aircraft Event Illness / Injury; Flight Deck / Cabin / Aircraft Event Smoke / Fire / Fumes / Odor
Flight Crew Landed in Emergency Condition; Flight Crew Returned To Departure Airport
Aircraft
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On climb out from ZZZ; we experienced a very strong fumes; similar to burning tires. The Captain was the Pilot Flying and I was the Pilot Monitoring and autopilot was engaged. Passing through 18;000 [feet]; I walked around the supernumerary area to see if I could detect a source or see smoke. I saw nothing but the fume smell continued to get worse; so I returned to the cockpit and got back in my seat. The Captain and I both then said we could taste it and I started experiencing a burning sensation in my throat and mouth. We immediately donned the O2 masks; [advised ATC] with ZZZ Center and got immediate return vectors to the FAF for [Runway] XXR at ZZZ. We accomplished all normal checklists to an uneventful approach  and landing. We kept the O2 masks on until after engine shutdown and subsequent inspection by the CFR unit at the airport. After leaving the aircraft; both the Captain and I experienced a headache along with a burning sensation in mouth and eyes so we sought medical attention where we were examined and subsequently released.
Air carrier flight crew reported smoke in the cabin and advised ATC for return to departure airport.