What kind of support system do you have around you? Are you married?
If so, can you work out a system with your husband to take the kids for an hour or so a few days a week so that you can hit the gym, or even just go for a walk around the neighborhood?
Can you get up early to do these things to avoid the heat?
Sounds like you could use some "me time" since you say that does make you feel better. Doing so much for others can be exhausting mentally and physically. I highly recommend making yourself a priority even if it's just for 2-3 hours per week wherever you can find it.
Have you talked to your doctor about other anti-anxiety solutions? I tried Wellbutrin, and other medications, fifteen years ago and while it did seem to help with some of my mood swings, it also made me a zombie. I personally hated it, quit all those meds, and haven't looked back since. I still deal with anxiety and depression, especially in situational bouts (losing job, illness in family, etc.) but I made the choice to work at it with cognitive therapy, watching what I eat, exercise and meditation. However, I don't have kids.
But all the advice I've every received from "professionals" applies to anyone with or without kids, or spouses, etc: If you're not making time and taking care of yourself, then how can you be your best helping others?
I'm with PdxMan: try introducing some healthy carbs in small doses you're comfortable with (green veggies, black Beans, quinoa, etc.) The thyroid needs carbs to function properly, but not the starchy refined carbs. If the thyroid is sluggish, that could be waning on your energy. And do try to work in a walk here and there, even if it's for 5-10 minutes in 95 degree heat. I grew up in the south, I know what it's like. Put on the sunscreen, wear light clothing, bring Water, and soak in the Vitamin D. It will do wonders!!