For your domestic trip, the best thing to do would be talk to the airline and the airport(s) you'll be flying through. If there are special forms or whatever you'll want to get those taken care of ahead of time. I don't know what the rules are about coolers anymore, so you'll need to get that figured out, too. I would also get a letter from your doctor to take with you. And leave plenty of time to get through security. An awful lot of stuff is at the descretion of the screeners these days, so even if you've got everything they told you to have, you still might have to ask for a supervisor to get it passed through. Or, they may not even blink. Who knows anymore.
You might also want to check with the drug company- would sending Humira through an xray machine damage it in any way? If so, it will have to be hand screened.
It shouldn't be too hard to find people to explain what the security process will be. A lot more people are taking Humira these days- you can't turn on the TV anymore without seeing a commercial for it. I'm sure the airports and airlines deal with passengers flying with it and other injectable meds constantly.