".....Don't share personal care items. Many items that we use on a daily basis will occasionally be exposed to blood. Often people will cut themselves while shaving, or their gums will bleed while brushing their teeth. Even small amounts of blood can potentially infect someone, so it is important not to share items such as toothbrushes, razors, nail and hair clippers, and scissors. If you are already infected with hepatitis C, make sure you keep your personal items, such as razors and toothbrushes, separate and out of reach from children....."
So there is a risk here but I certainly cannot quantify it. I will say it's more likely than not that you are not infected but there is no way to be sure.
There are basically 2 tests that are used to determine HCV infection.
Generally the first test patients undergo looks for antibodies to Hep C in your blood. If the test is positive it means that you have been infected with Hep C at some point in your life. It can take as little as a couple of weeks and as long as several months to show antibodies. This test, however, does not determine whether you are currently infected. Some people do clear the virus without treatment but nevertheless carry the antibodies in their bloodstream for life.
The test to determine whether you have an active infection is called a HCV RNA PCR test. With this test you can test as early as 1 week or 2 after exposure and if you're infected it will show. Unfortunately this test is rather expensive and on the basis of your possible exposure it is unlikely a doctor would order this test without ordering an antibody first.
My advice is to wait and have an antibody test in a couple of months and go from there.
I also strongly advise that you find another barbershop that is sensitive to the risk of infection and cleans their equipment properly.