Should we avoid competing with products that Amazon sells?

I wouldn't avoid selling your own brand of an item. Simply add it to your research list and complete the rest of the process to see how it scores. Sometimes Amazon's listings leave a lot to be desired, and they are not always the best priced, or offering the best value. The other side of Amazon selling something is that it is normally a branded item, therefore they will be very slow to react to somethings that you do correct, such as adding bonuses and/or increasing value.