If one increases in improving himself, is it normal to not want to interact with others out of fear that they might have an evil influence on him

Don't go to extremes. Do what you just said you're going to do with people you know will influence you in a negative way, so that you can protect your religion. However, there are many good people who are better than you. You can interact with them and get closer to them so that they help you improve yourself, and you can encourage one another in goodness.