I would recommend that you try the Cerave hydrating skin cleanser and lotion as a facial moisturizer. Cerave is available at any pharmacy or grocery store in the facial moisturizer section. I use the Cerave lotion for both my kids, from the time they were newborns, and both my kids have sensitivie skin. When my kids were infants I also used this on my face, so I wouldn't expose them to any other harsh chemicals, and I really liked the way it worked.
I have been grappling with sensitive as well since my teen years, and I can tell you that the trick to dealing with sensitive skin, is to stick to one simple cleanser and a thin, light moisturizer. In TX, there is no need for a heavy moisturizer with all this heat and humidity. Also, try not to experiment too much with various moisturizers. I find that SPF lotions are extremely irritating to my skin, and my eyes burn just like you described.
You can get your SPF protection often from some powders (like Almay which makes a nice powder with SPF in it), which is much more tolerable than the lotions, which sting. But for a while, stay away from the SPF chemicals, and just let your skin settle down.
All the best, and remember, care for your face the same way that you would care for your baby's skin - mild, not too harsh or exfoliative, and consistent - your skin should get better within a few weeks of consistent gentle care! good luck!