Can streptococcus be caused by unsterile instruments from going to the dentist?

Less likely: There are many types of strep, some of which (viridans for example) commonly colonize the mouth. Occasionally, particularly if there is a break in the skin or immune deficiency, infection can occur. It seems much more likely that a strep infection in the mouth after dental procedure is from bacteria already there than from poorly sterilized instruments.

Yes: Strep and staph and other bacteria can be present on non sterile insets.

Yes: Any type of bacteria can be present on non sterile instruments as well, as normally present in the mouth.

Possible, but...: Considering the rigorous sterilization etc uniques employed by Dental offices today, the risk of cross contamination is extremely small as long as the sterilization chain remains intact. Greater risk that any bacteria based problems are from bacteria already inhabiting the host's mouth.