The 8mg/2mg means that the Suboxone strips you're taking contains 8mg of buprenorphine which is the opioid and 2mg of naloxone which is basically an anti-opiate. When you take naloxone orally, like you are doing, it's inactive so the naloxone won't do anything for you. It would only be activated if you would try to shoot it.
If your doctor is telling you to take two 8mg Suboxone strips per day I'd say he's crazy or has no clue what he's doing. 16mg/day for someone who has a fairly mild dependence as you have is way too much. Normally you start with less and go up if needed. I'm not a doctor and I don't have that much experience with Suboxone but based on what I know I would think that you could do just fine on 4mg - half a strip. If you take too much you won't feel good. You'll often get jittery like you've drank too much coffee and some get anxiety. If I were you I'd talk to the doctor about lowering the dose and see how it goes. If you need an increase then get one but there is no reason to start out taking more than you need.
There is a pretty good site that is ran by a Suboxone doctor and focuses on Suboxone only that you may want to check out. The doc will take questions too. It's called suboxforum. You can google it. I can't post links.