Shifting between upper and lower body workouts is an excellent and fairly common way to strength train. And it's the method I myself am currently using. I hit my upper body one day, take a day off to run, then hit my lower body and repeat. The logic? Your muscles have ample time to rest in between sessions.
What to do if you get bored or hit a plateau? Switch it up! But unless you have a trainer, it can be hard to come up with new exercises. So try this: Stick with your routine, but reorganize it. Divide individual exercises by front and backside muscles instead of upper and lower muscles.
Sounds crazy, but I think it's a good idea. Work your front deltoids (shoulders), chest muscles, biceps, abs and quadriceps in one session, then switch to your rear deltoids (shoulders), back muscles, triceps, glutes, hamstrings and calf muscles in the next.
Just make sure to hit both sides of your body equally for obvious reasons.