There are definitely shelters you could stay at, but if you cant make it in time for a room it is possible.
Try asking the male employees at your job, especially the married guys. They'll be more willing to help you, but if no one is willing to lend a hand here's my advice.
For only two weeks you could do it, I have a pal that did it for a lot longer. As soon as you get off work try to hang out at places like McDonalds or whatever that are open all night and hang out while trying to get as much sleep as possible before they ask you to leave, then just go to another one and do the same. Try to sleep while sitting up, if you have headphones it makes it look like your listening to music. Also you can get on the bus and ride it all the way to the end of it's route then back to were you came from to get sleep. During your lunch break try to get in as much sleep as possible, and eat when your out after work. Try to stay up as much as possible during the night, you won't get much sleep anyway if you tried with all the noise.
It's important that you try not to sleep on the street during the night, try to keep walking around as much as possible. The cops usually will take you to jail to sleep but it will be hard getting out because they'll ticket you for loitering. It's a bait and hook technique that's why most homeless people sleep in places where it's hard to be seen at night. The chances of you getting raped or some random person coming up to you and jumping you are pretty slim despite the preconceptions people have in there heads about sleeping on the street.