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No problem. I was also a bit of a punk and had to do a lot of research on how to dress for the career I ended up in. Also riding my bike to work I find that these things are awesome if you have to switch between manual labor and wearing a nice shirt. Good luck on the new gig, it gets easier as you get into the flow.
There's science behind why we/cyclists continue to sweat after a ride moreso than other sports, but it isn't related to health or hygiene at all.
If you're able to get to work an extra 10-15 minutes early you'll be able to cool off & stop sweating. Afterwards clean up with something that kills the microbes that cause B.O. (baby wipes, "showers wipes", hand sanitizer, etc.) and no one will know you cycled in that morning.
2 Miles isn't that far. Depends on how fast you're going but I don't see why it would take you more than 15 minutes unless traffic is bad. Would you have access to a shower/locker room? If so just leave early and shower before class. If not, Nathan Power Shower wipes are a fairly cheap and simple way to freshen up real quick.
Until you find a real shower, they make cleansing wipes that do a pretty good job (I use them hiking), so those with a fresh set of clothes could get you by until after your class. https://www.amazon.com/Nathan-Cleansing-Deodorizing-Outdoors-Refreshing/dp/B001CJVK6Q
Though I agree, there should be an easily accessible shower for you, good luck :)
Something like this for use while you are unable to shower:
I usually end up having to pack everything into my commuter bag and drag it in every morning with me. There's not a lot of space to store extra clothes at work.
My routine last year was to bike in, change in the bathroom and use these things to freshen up.
Then at the end of the day, I'd repack my bag untuck my shirt and ride home. Being oddly lazy on the way home I'd ride in whatever I wore at work, resulting in destroyed chinos. If I can't find some good options, I'll just commit to changing in a public bathroom at 5PM. Somehow I'm fine to change there in the morning because they just cleaned but by 5PM it looks like this.
shower first. ride. towel off or use summa deeze...[link]
Shower Wipes // eHow
Personally I've just worked out after work, UA would help dues to it absorbing sweat. The wipes in the link would help I don't know if they're the best bet though.