Corrections or counter arguments are welcome.
Any backpacking first aid kit should have basic treatments for wounds. That's absorbents (strip bandages, gauze pads, etc.), things to hold them on (roller bandages, adhesive tape, and maybe tincture of benzoin to make extra sure the glue holds), and wound closures (butterfly strips are the standard, but you can made DIY butterflies out of duct tape or what have you, or given a high tolerance for pain, dental floss and a fat needle can work, and cyanoacrylate-based glues like Krazy Glue can hold deep cuts closed). For musculoskeletal injuries like sprains, Ace-type compression bandages are always key, and chemical cold packs are good for keeping swelling down (mountain streams can work, but they're in short supply in the desert). For severe sprains or worse, you can't always count on finding big sticks for splints in the desert, so a SAM splint or air splint is worthwhile, especially for rough country. Medications are your own business; you know better than me how many painkillers, antihistamines, antidiarrheals, etc. you need.
As for the desert specifically, extra bandages can't hurt (the desert is full of sharp things). Some such sharp things are best extracted with a good set of tweezers, while glochids (tiny, almost hairlike thorns that feel like Charlton Heston's knife collection in your skin) can be removed with duct tape. It's my understanding that dry places don't breed infections the way rainforests do, so antibiotics probably aren't as crucial. With dry air and blowing sand, eye drops are good to have. Electrolyte replacement tablets (make sure they have plenty of potassium as well as sodium) help some people, but some people do fine without.
A lot of people worry about venomous snakes in the desert, and if you can get the thing assembled within a minute of the bite, a <A HREF=http://www.rei.com/product/692.htm?vcat=REI_SSHP_CAMPING_TOC>Sawyer extractor</A> might be useful. However, there's no good way to remove venom later than that. (DO NOT EVER cut a bite to get more blood out. It makes things worse.) Some doctors recommend tying a bandanna or length of cord around a bitten limb, tight enough to slow circulation without cutting it off (make sure you can still fit a finger or two inside). Others say that localized tissue damage is more severe if you do so, and letting the venom thin out in your bloodstream will cause less long-term damage. However, the most important thing to remember about snakebites is that VERY FEW BITES FROM VENOMOUS SNAKES INVOLVE A HARMFUL AMOUNT OF VENOM. People don't swat flies with hand grenades, snakes don't waste venom on things that will leave after a dry bite. So calming down is the best treatment available. If the snake does inject venom, you'll need to know what kind of snake it is so doctors can get you the right antivenin, so a field guide is another key item.
I'm probably insulting you by pointing it out, but just to make sure, you can't go overboard on water. It's not possible. The worst medical risks-- dehydration, heat stroke, etc-- are all prevented with water.