JDitto on everything Tulip said. I often drive all of my clothes to work at the beginning of the week; I have an office and our locker room has lockers so i dont have any issues storing my stuff. Yes, i blow dry my hair after I shower once i get to work - like you, i sweat a lot so i have to shower and my hair doesnt dry well on its own.
I have a commuter bike with a rack and panniers when i need to transport on the bike, or i'll bring my road bike to work on my car along with several days of clothes and ride my road bike back and forth if i'm training.
As for those jerks in the car, they can take a flying leap. You're doing something you enjoy, and increasing your fitness as you do it. Dont let people like that scare you; sounds like you've already got solutions for your other fears.
Just do it, and have fun. Commuting by bike always makes for a good start to my day enjoy!