In general, you are allowed one "full-size" carry-on bag (such as a small suitcase or garment bag) and one "personal item" (such as a small backpack, purse or briefcase). If you're talking about a smaller backpack, you should be OK with that and a small suitcase. Some larger backpacks wouldn't qualify as a personal item, but you may be able to get it on anyway (to the chagrin of your fellow passengers, however, so be courteous).
On most larger aircraft you'll be able to take those items into the cabin and stow them in the overhead bins and under the seat in front of you. If you're on a regional jet or smaller plane (probably not likely out of Dallas, but possible depending on what airline you're on), you'd need to leave your larger carry-on item on the jet bridge and stow your smaller item in the cabin. The item you check outside the plane will be delivered to you as you leave, so you don't have to go to baggage claim to collect it.