Hello. I'm not a medical assistant or phlebotomy technician, however I just wanted to suggest perhaps applying to local medical laboratories. Also various doctor's offices seem to need medical assistants. You may want to apply to some general practioner's/internal medicine offices. They're so many of them around.

Or perhaps you can get experience working in a chiropracter's office, in the meantime. I know that you probably won't get hands-on experience much clinically, for ex., in phlebotomy (drawing blood for others that may be reading this :-) or perfoming EKG's and such. However, at least you may get experience in a health care setting working directly with patients, the front office, perhaps implementing physical therapy-type treatments such as heat packs, and dealing with outside insurance companies. Just some "food for thought." Good luck to you!