Your parents don't owe you a ride. How far is the commute? Is it uphill or downhill (or both?)

There are several options. Can you walk, or take a bus? Or you could ride your road bike slowly so as not to sweat. Carry your work clothes in a backpack and towel off and use baby wipes to clean up before changing. Get a second, beater bike for $100 or less if you can find one and ride that to work.

I ride in my office shirt and shorts, and my ride to work is mostly downhill so I go slow to avoid sweating. Then I just change into long pants. You can roll up long pants and they later come unrolled without much wrinkling. If there is a locker at work you could leave your work clothes there. Just don't take them home to launder and forget to take them back.