Does celebrex (celecoxib) contain any blood thinning medications?

Not exactly. Celebrex (celecoxib) is a nonsteroidal anti-inflammatory drug (nsaid). The nsaids are felt to have some "blood thinning" properties, and they can increase the risk of bleeding particularly when taken in combination with true blood thinners such as warfarin.
No. Celebrex (celecoxib) has no platelet inhibiting effect. In fact, to the contrary, there is a small risk of blood clots (heart attacks) with celebrex (celecoxib). The biggest risk, however, is bleeding - not because it's a blood thinner but because it damages the lining of the stomach .