Yes, it is bad to swim with nicked eyes which will may cause eye infection. As we know, there is the bacterium in the swimming pool. If you don't wear the goggles, you will get the high possibility to get the infection for the eyes. You'd better wear the goggles when you swim.
Yes, it would not good for your eyes. In general, most people would swim in a public swimming pool. It is risky for you to get any contagious eye disorder from there.There is high possibility for your eyes to get injury as well. Hence, you should protect your eyes by wearing swimming goggles. It is a functional tool that is specialized for swimming. It not only prevents any invisible bacteria or virus to enter your eyes to make infection or irritation, but also avoids any injury that is made by visible foreign objects. Additionally, it makes you can swim with more fun.
Well, it seems that you are going to swim, good for you. So, as to your question, I would say, yes, probably. The reason why you might have some bad impacts on your eyes is that some swimming pools are not refiiled and cleaned on a regular basis. Some businessmen want to cut their costs. So, your eyes might be infected if you have no goggles when swimming. So, I suggest you get a pair of goggles, just in case.