If I fell in a laundromat, can I get anymoney?

On what grounds would you get money?

First, the mere fact that someone injures him- or herself in someone's store or on their property does *not* make that person liable. There must be fault for liability; that means the store owner must have done something wrong. A common slip-and-fall example is when there is a spill in a grocery store and the store knows about  it but doesn't mop it up; in that case, the store carelessly created a slippery condition, and so is at fault. But if you tripped over a chair, unless you feel that the store owner or her employee(s) careless left the chair in a dangerous position, there would be no liability--and if you felt that, you'd need evidence to prove it, and you could also face the hurdle of explaining why you are not also at fault for not seeing the chair in front of you.

Second, you can only recover compensation for your actual economic losses and injuries. With nothing broken and just some pain, likely the most you could get, even if you sued, would be the cost of the ex-rays and pain killers, which is likely not worth the cost of suing.

And, of course, if the owner has no insurance, if you did win anything, it would come out of her pocket.

You could sue the owner of the laundromat for negligence.  When you complete your medical treatment and are released by the doctor, obtain your medical bills and medical reports.  The medical reports will document the nature and extent of your injury and will be used to determine the amount of compensation you receive for pain and suffering.  Compensation for pain and suffering is an amount in addition to the medical bills.  Compensation for the medical bills is straight reimbursement.

You will need to file your lawsuit prior to the expiration of the applicable statute of limitations or you will lose your rights forever in the matter.

You said the owner of the laundromat rents.  You could include the owner of the building and the laundromat in your lawsuit for negligence. 

If the owner of the building has insurance, you could file your personal injury claim with their insurance carrier prior to filing your lawsuit for negligence.   Your personal injury  claim should include your medical bills and medical reports.  If you are dissatisfied with settlement offers from the insurance carrier, you can reject the settlement offers and file your lawsuit.  Again, you will need to file your lawsuit prior to the expiration of the applicable statute of limitations or you will lose your rights forever in the matter.  If your case is settled, no lawsuit is filed.