That hill does look like a bit of a beast, but time will tame it. Have you been able to find other routes to avoid that intersection? Is there a bus that you can hop on to avoid the hill and intersection, many here do multi-modal commutes.

Commuting year round isn't a problem, I like in Vancouver and I have no issues riding in the rain. Some days are colder and more wet than I like but I do it, and I always had the bus on really nasty days.

Who cares what others think?

Is there a gymnasium at school that has lockers? Or lockers you can rent anywhere at school? Showers? I used to rent a locker per semester at the school gym and that was a great home base for leaving gear like a shower kit, shoes, and clean clothes

Just give it time and figure out what works best for you is the most important thing. Those miserable days that you successfully commute will build into being little badges of courage.

But remember being safe is the most important thing. Wear a helmet.