Should hospitals be allowed to use and share your genomic information collected in blood samples without your consent?

Of course not! Genomic and personal information are indeed ... well, personal, and they don't have the rights to share because it is something no person should butt in and know about. This is the reason why for most surgeries, they get consent from the patient to let the hospital know that the patient will let the doctors do the surgery. If they share it, they may even get sued.