Is this normal that my eyes turn red when I wear my contact lenses for too long?

Maybe. It could be your eyes telling you they need a break, more common after extended wear or with underlying dryness. It could also be a reaction to solutions or protein buildup on the lenses. You need a thorough exam to diagnose.
No. Neither one is normal (wearing contacts for too long or the eyes being red). I will say it's a pretty predictable reaction, though. The eyes turning red are likely the first indicator of the cornea revolting at the relative lack if oxygen that it is sustaining because of the prolonged contact lens use. This can set you up for corneal edema, inflammation, and overwhelming infections.