There was no risk...
I concur, no risk from this event. You used a new needle and a new testing strip, so no one else's blood came in contact with your body.
You don't even know if your family member has Hepatitis C - and even if they did, it would still be a no risk situation.
To put this in perspective, in health care settings, doctors and nurses who accidentally stick themselves with a needle that has just been used on a patient that they know is Hepatitis C positive only are infected at a rate of less than 3% of the time - 97% of the time, nothing happens. What happened to you isn't even close to a bloody needle stick, so your odds of becoming infected are non-existent.
No need to get tested for this. However, the next time you get a check-up, you may want to have your doctor run the test for Hepatitis C just to set a baseline in case you ever have an actual exposure in the future so you can say "look, I was tested back then and it came back negative". You might also want to have an HIV test (and other STDs if you are sexually active) for the same reason.
No need to worry. Go an enjoy your life :).
There is no risk in your case