Getting Rid of Bed Bugs Without Chemicals

Do a search on Diatomacous Food Grade. According to the reviews it will get rid of about anything and will not harm people or pets. It's sold on the internet or at Home Depot, or Garden shops and is reasonably priced.

Bed bugs can survive for up to a year without feeding on a blood source, so figuring out how to kill bed bugs is a real challenge. These parasites are able to hide in small cracks and crevices, are difficult to find, and even harder to eradicate. Females can lay up to 300 eggs, which hatch within ten days, thus creating an ever-growing population.
Once an infestation has occurred, patience and persistence is the key to ridding the area of bed bugs.

When choosing a professional bed bug exterminator, be careful! Many companies that only specialize in how to kill bedbugs aren't as qualified as full-service pest control companies. Your best bet is to find an established pest control service company that has been in service for at least five years, and you might also ask around and see if anybody you know or look at review sites (like yelp.com) to see if there are recommendations for any specific pest control services.

Make sure the pest control company you choose is certified in your state. Exterminators can be pretty expensive; expect to pay between $250 to $1,000 per room. You'll also want to make sure you choose a pest control company that will make follow-up visits, these are usually necessary for bed bug elimination. Bed bugs are nasty critters and can cause serious illness. There is an apartment complex near me that had to have the tenants throw out ALL of their furniture and rip up the carpeting before the exterminator began his work because they are so difficult to kill.
I would urge you to beg, borrow or steal (well, not steal) the money to hire an experienced exterminator. It will be well worth it.

I read that tea tree oil will get rid of them. Maybe spraying it on the floors will help.

I don't know if there is a remedy that you can do yourself for bed bugs. From every thing I have heard it takes an exerminator and more than one treatment.