How many times have you worked out one day and then woke up the next day feeling like you'd been run over by an 18-wheeler? And how many times have you put off working out because you were in too much pain? And how many times have you given up completely because you missed a day or two because then you weren't doing it "perfectly"?
I would have to say yes to every single one of these questions. I have started and stopped more workout programs simply due to the fact that I was sore from working out. And if I missed a workout due to soreness, I was a failure. Now, I don't mean actually injuring myself, but soreness. There is a distinct difference there.
Working to soreness is muscular, it tends to stop hurting when you stop moving. Injury is when you hurt to the point that the pain does not go away. In my experience I have noticed injury happens more on the bone/joint level, but can happen in the muscles as well. You should never push to injury, only to soreness and muscle failure.
All of this being said, what do you do when you are sore to the point that you don't feel you can work out? The big secret is to stretch!
After my first day training for C25K I was sore to the point that I found it hard to walk the next day. I had no idea how I was going to get on the treadmill again for day 2. I was in a great deal of pain and soreness.
My roommate/trainer had me use a foam roller to work the muscles out and it helped a great deal. But yesterday, after day 2, I decided to spend an hour doing the P90X Stretch video. That was the best thing I could've done for myself and for my training.
When you stretch your muscles out, they are far more forgiving when you want to use them again. I was able to get on the treadmill for a warm-up to today's strength training with no problem. Did I still feel a bit of tenderness in some of the muscles? Certainly! I am working them in new ways, and more intensely than ever before. If I felt nothing at all, then I wouldn't be doing it right!
My advice is to find a really great stretching program, or even try something like yoga. Anything that will give you flexibility. It will reduce your pain a great deal post-workout. It will help your muscles to recuperate much faster and keep you moving towards your goals. Don't discount it because you're not huffing, puffing, and sweating your ass off.... it will help you more in the long-run than you could ever anticipate.