Hello, ACWright . . . it is possible. At least it is for me.
I have had bad colds and flu, and even abscessed teeth without running a fever. I seem to have simply stopped running fevers about ten years ago when sick. I know that my metabolism changed at that time because I lost a tremendous amount of weight back then and not sure if there is a connection with that or not.
It could be the flu or it could just be a very bad cold virus. If it lasts longer than ten days, it may have turned into a bacterial infection which you would need to see a doctor for.
Let us know how you are doing!