Not sure if the bike makes that much of a difference. I have a nice road bike and get passed all the time. Sounds like you need to concentrate on the clothes with the right layers and go at a pace to arrive a school without a lot of sweat. Don't worry about the other cyclists - just pay attention to the traffic so you arrive in one piece. If anything, some higher pressure better tires. Unfortunately, a new road bike will probably be quickly stolen at your school even with a good ulock.
Visit your local bike shops and try out a variety of entry level ($500+) road bikes. Eventually you will want two bikes - one for commuting to school where if stolen won't be a big loss and a nicer road bike for longer rides on the weekend.
Have fun!