Those plants you had success with are perfect for Texas and will grow no matter what you do. Carrots need lighter, sandier soil to grow their big root into the ground. Peas take a lot of room, you don't get much for your effort but I like to eat them right out of the garden. I had success sewing them in early fall so the seeds and seedlings could be warm but the mature plants could be cool. I like growing cool veggies in the fall. Tomatoes, onions, and radishes I have all grown with success but maybe they don't like the chemicals.
Better veggie growing:
Find good compost. Generally the best stuff costs more but it's worth it. Have a pickup? Living Earth Technologies has it at a bargain per pickup load. Mound this up as your soil. Add to the top inch or so lava sand, green sand, rock powder, cornmeal, molasses, and humate. Most import of those is the cornmeal and molasses but they all help. With good quality compost you shouldn't need to fertilize but a foliar feed would be good when the plants mature.
Never use peat moss. It is a dead material and is expensive. Top soil is ok but it's better to put money into compost which is like super fertilized top soil. Cow manure is alright but the cheap stuff sometimes has weed seed from the plants the cows ate.
I hope I helped. Ask more questions if something isn't clear. I don't even have to say good luck if you use organics because it always works!
