Am I qualified to work as a lab tech in a medical laboratory?

Most hospitals require a certification as a Medical Laboratory Scientist (MLS) or a Medical Laboratory Technologist (MLT).  Since you have a BS you can get your MLS certification (associated with a 4 yr degree as opposed to the MLT which is a 2 yr degree).  It's usually about a year to 16 month long program that's designed to be a final year in finishing your degree.  I got a degree in Biomedical Science then went into a certification program and got my second degree in MLS along with my certification.  College of American Pathologists is the overseeing body for labs and they require anyone doing moderately or highly complex testing (anything beyond a basic pregnancy test) be certified.

You might be able to get a job as a processor in a micro lab setting up plates and such, but you will not get to work a bench as a tech.

If this interests you I'd also advise you to look into getting certified in Molecular Diagnostics.  Its a really interesting field that uses latex particles coated with engineered antibodies to various analytes to test for substances in samples.  It's an incredible field and (in my opinion) where all clinical testing will eventually end up.  

Hope this helps