How can I calm myself down in very claustrophobic situations?

I'm 19 years old and started University in 2012, so I'm now living by myself and no longer at my dad's house. I've got a small apartment but, obviously, not my own washing machine.

That in itself is no problem as there are some in the basement of the building I live in. What hinders me from using them though is that I tried getting into the hallway leading to the laundry room a couple of times now and I just can't get in there.

I remember being extremely scared of small closed rooms, such as public restrooms and elevators, ever since kindergarten and (whenever I have a car) I don't park in underground parking spaces either. Usually, I can overcome my fears though. It takes me somewhat long but whenever I'm usually able to enter small spaces. I just stand in front of them for a while, look at them, take deep breaths and reason that nothing bad is going to happen to me - even though it feels as if I won't be able to leave again once I enter.

Now with this basement, it's different. It seriously looks like endless tunnels I'm trapped in in some of my nightmares. It's pretty dark and the lights don't work via a motion detector, so they turn themselves off after a while, no matter whether anybody is still in there or not. Furthermore, the basement connects three huge buildings, including underground carparks, with each other and they are a little bit like a maze. The person connecting me to the Internet had to do something down there and got lost for about 30 minutes.

I'm currently taking the bus to a laundromat that is downtown, but it's inconvenient, (a very little bit) more expensive and I just feel stupid for making that much of an effort, just because I can't get to the washing machines on my own. I've been down there with others, because it helps me stay calm, but I obviously can't call a family member every time, asking them to drive all the (250 miles) way to accompany me through a creepy basement.

Are there any other ways to stay calm? I feel like one of my biggest problems are that:

-the lights can go out any time and I'm terrified of standing in the middle of an almost pitch-black tunnel all of the sudden

-once I get in there, I'll have to return at least two times to use the drier and then pick up everything to carry it back to my apartment

-I just can't convince myself that I'm going to survive. I have no clue why, but it feels as if I was going straight into my own grave.

I'd be thankful for all the advice you could give me.

Oh, and I can't go to a psychologist right now. I'm not sure whether my insurance covers it and I also don't have time because my finals are coming up and I'm rather busy.