Hi, you are right that your son's behaviour reflects anxiety. It might be that there are changes around him in school, perhaps a new teacher or a new child who just joined and is presenting him with challenges. It may also be classmates teasing him for something. It's hard to say what exactly is the problem, so I guess you do have to continue to monitor to find out the root cause. If your son is at the age when he can talk, 1) do acknowledge his feelings and offer your support saying that "I am here to listen, and if anything is difficult for you in school, I want to help you." 2) Understand that rubbing his hands and putting fingers in his mouth is a way of self-regulating his anxiety. Scolding him will not help him to stop. You may try to offer a substitute like a comfort blankie, or give him a hug and rock him gently to soothe him.
Hope these helps, and wish things will be better for your son soon!