If you're an EMT-P, you shouldn't be asking, you should be telling...
I'm just a lowly (out of cert) -A, but this is what I carry...
4x4s, vaseline 4x4s, a couple 8x10s, roll of gauze, squirt bottle of saline with the tip cut larger, bandaids, tape, emt scissors, tweezers, gloves, ace bandage, sanitary napkins in a baggie, baby wipes in a baggie, paper towels in a baggie. and i have a little 'snivel kit' in there as well.
i don't carry any splints because there's enough in the woods; i don't carry a breath mask but probably should.
oh yeah, some duct tape - not a full roll; sliced in half and re-wrapped around an old micro-pore roller....