My bathtub immediately starts filling even if you only take a short shower. What are the health effects?

I live in a very old building and there have been numerous attempts to make the water drain correctly. From basics at the source (my bathtub, there are other tenants in the building that have issues in sinks, etc..it varies) to outside plumbing work and snakes, chemicals, and who knows what else..ultimately, the water drains very very slowly at best..This has to be old water coming back up from previous uses since it's coming so fast right? What health risks are involved in this? I'm concerned esp. b/c there has been an outbreak of MRSA before...I'm a renter, the landlord has definitely tried to handle the problem but it never lasts longer than a day or two..