1. Bring your own shade.
Sunglasses, a wrap, a Chinese fan, an umbrella stashed in secret purse pocket. Remember that you're not supposed to bring an umbrella so make it a cheapie one you can toss if it gets caught. Those collapsible kind from the 99cents store are great.
Turbans are cool because they're light and you can wrap them around your head, wet them for cooling down and lay on them later in the day. Also if you're prone to allergies you can cover your face when you're walking from dusty parking lot to fields and back. Hats are cool, but they suck to carry at night so I wouldn't recommend them unless you can bear to lose it once the sun goes down, you also don't want to be blocking people's view during the day.
Bring the shade, don't be shady.
2. Chapstick, lotion, SPF sprays, tiny hand sanitizers.
I just bought this fresh cooling SPF Neutrogena spray with 45 SPF . I like to bake because my skin doesn't turn color (beige Mexican) so I slather on the coconut sun tan cream at home and retouch with sunblock throughout the day.
3. Candy, gum, water, gatorade.
You are allowed to walk in with a sealed bottle of water but you're not supposed to walk in with sports drinks. The key is to stay hydrated without paying 2 bucks for every bottle your body needs. Keep sweets to keep your dry mouth happy. Also think about carrying a plastic bag (grocery) to collect empty water bottles. Coachella has a recycling program where you trade in 10 empties for a new bottle.
Not fun but manageable if you stick to the trailer potties behind the regular ones. Once in, there's a little fan on top of your toilet, use it. Take advantage of the running water and wash your hands good (not to drink). Toilet paper may run out so carry some tissue/napkins with you also.