AZfiddle, I did what you are doing 1-2x a week for 5 years. I was also a teacher and I also made the choice to ride my road bike instead of my flat bar road bike with the pannier, because it was so much lighter. One thing that helped was I brought all of my hygiene supplies to keep at school and also a spare pair of underwear, black flats and a pair of capri pants and a black jacket. I would bring my clothes for the week in on Monday, but I also knew I had the extra stuff there, so I could just bring a t shirt with me. Another thing I did that made it easier was I showered at home and then "cleaned up" when I got to school, in the bathroom, put some make up on, and put gel in my hair. I didn't have to bring a lap top, so I used my Camelbak with the bladder taken out for a backpack. It was more anatomically correct than the other ones I had and I could easily get my lunch and a few papers, make up in there.
Commuting 1-2x a week kept me sane!