Is This Chicken Fully Cooked?

Yes, the chicken is fully cooked. The internal temperature of chicken when cooked all the way is 165 degrees, so you may have actually overcooked the chicken causing it to be dry. As far as the redness you found in the chicken, it sounds like it was a prominent blood vessel, its rare that you don't find redness in chicken when its fully cooked. So don't worry, keep cooking :)