FWIW, you might want to take a look at ridewithGPS. Mapmyride is notorious for - I don't know the correct way to say this, but their contour lines are very far apart, so they drastically underestimate grade and total elevation gain if you live in an area with short, steep hills. I don't have much doubt that your hill is a LOT tougher than Mapmyride says it is.

The other thing is, it's actually good to breathe hard and sweat. It is inconvenient to arrive at work all sweaty, I don't underestimate that at all. But if you're not breathing hard and sweating, you're probably not getting stronger... and if you are, then you are. Do you have someplace you can stash clean clothes at work - and if not a shower, then a couple of washcloths for a sponge bath?

Do make sure you're breathing hard on the hill - not holding your breath while you climb and then gasping for air when you reach the top. A lot of people do that on stairs.

Rather than letting the hill psych you out, try attacking it. You already know that you can ride the whole distance. You don't have to save energy for the unknown. So, why not ride the hill a little harder each time? Make it a fun challenge for yourself. That's how you get stronger.