You are on the Gulf Coast much as I am. Down here tomatoes are pretty much two season veggies, Spring and Fall. Tomatoes typically don't set fruit when the nights stay really hot, like ours do in Summer. So you either plant them really early or late for an early summer or late fall crop.
I looked in my Louisiana Vegetable Planting Guide I got from the Louisiana Extension Service (available for free online). Your climate is really close to mine. It gives the month of June as a good time to start tomato seeds for that fall crop. I'd probably wait a week or so to start them, get well into June.
You can start them inside where it is climate controlled or outside where you are subject to the weather. There are advantages and disadvantages to both. Indoors you need a lot of light, a way to water them and care for them that does not make a mess in your house, pets and small kids might be a hazard. Outside you have the weather to contend with. Heat, wind, and rain or lack thereof. They may drown in our torrential downpours but they don't like drying out either. By now, bug and other pests populations are growing, pretty well established. I'm not saying don't try it, just mentioning what challenges you might see. It may sound overwhelming but people do it all the time.
Good luck!