I'm wondering if the peroxide is causing more harm than good. It can be really caustic to the skin - especially the thinner skin of your penis, and kill off the good bacteria that might help keep everything in check, allowing the balanitis to get worse. At this point, your skin doesn't know what to do on it's own, so it's just sending signals to create more moisture, and you're just drying it out.
Try using a non-soap cleanser, once a day. It may feel really gross at first, especially since you are used to cleaning it so often. There are also really gentle soaps you can use. Here's a list of recommendations for people with eczema, but they should work for you, too -
You can also try one of the creams your doctor prescribed with it, but try eliminating the peroxide first. Do the doctors know you are using that?
How have you been doing with this? Smegma is normal and no big deal. It only comes in big amounts for a reason, one of those reasons being irritated skin, and a regime of peroxide and cleaning three times a day is really harsh. It's kind of like a woman repetitively douching with a chemical douche, she doesn't actually need to douche at all, and should never use anything except water if she does, or the delicate skin in the area will overreact.
My suggestion is to clean the area with just plain water, or maybe a mild saline solution (8 teaspoons to a gallon of water is a formula a woman wrote recently that she used for a perineal tear). And especially, not to bug it three times a day like you were. Have you laid off the obsessive washing and seen where you get?