Take rest days if you want to, but they're not mandatory for successful training or injury prevention. That said, you shouldn't continue to push your body day after day. When your running back-to-back, you need to be smart about it by adjusting your intensity. If you are training more than 3 days per week, some days should be easy, sometimes you should go slowly.
I wish I'd realized, at the time, that the fatigue which kept me from checking my watch was actually the consequence of not training effectively. This turned out to be equally true of my tunnel vision. As soon as I started training to heart rate, I felt more comfortable. I was listening to my body and working within my limits. I could look at my watch or around the neighborhood, even chat with other runners! For the first time, I was actually able to enjoy myself and experience flow when I was running.