When you go to the hospital and they take blood samples do they look for std's and other diseases?

Not automatically. Unless either the patient brings up the topic or there are other factors at work (e.g. known HIV infection), the doctor will not have all blood samples tested for STIs, as all laboratory tests take both time and money which must be conserved whenever possible. An exception to this rule exists when donating blood; in this case blood drawn is tested for a wide assortment of communicable diseases, including most STIs.