http://www.delta.com/traveling_check...lies/index.jsp

Some medical items can be carried on the plane, along with the regular carry-on allowance, as long as they meet the standard size and weight limits.

The 20x12x12 is going to be a problem, though:

Baggage must fit easily in the Carry-on Baggage Check, which is located near the check-in counters and at the gate and is approximately 22" x 14" x 9" (or 56 x 36 x 23 cm).

Probably ought to replace that bag with something compliant with the above dimensions.

In the somewhat likely event that somebody tries to deny the medical supplies, ask for a Complaint Resolution Official (CRO). Each station is supposed to have a CRO whom is familiar with such regulations.

So, laptop bag, size compliant carry-on with clothes, and bag with medical supplies should be good.

David