Social Anxiety over laundry?

I just discovered that I have severe anxiety regarding doing laundry anywhere but home. We now have enough people living in our building that it's tough to get time to do laundry with only 1 washer and 1 dryer for about 13 people (btw, it's only a 6-bedroom apartment building). It also doesn't help that quite often the others start laundry and then leave, actually leave home. This means that the laundry can sit forever before they return to finish. This is the situation today. I have 4 loads of laundry to do but can't because both the washer and dryer are full and no one is home in the building but us. There is always the option of the laundromat (which of course is twice as expensive) and I have several people who have offered in the past to let me do laundry at their homes. Both of these options have left me in a panic. I am forced to realize that the idea of going to someone's home to do laundry makes me feel obligated to socialize, something I'm not comfortable with in normal situations, let alone that I'm now in someone else's home using their resources, for hours at a time. The laundromat freaks me out because, unlike stores or crowded places, people aren't necessarily minding their own business, doing what they need to do, and getting out. They have time to watch me and possibly criticize. I know, logically, that they might not be; and even if they are, it doesn't really matter. It's hard to ignore the thoughts in my head that say otherwise, though.