If it were me I would contact her and give her a heads up that I was feeling sick and might need to cancel tomorrow, and either try to reschedule for later in the week or agree to contact her in the morning and let her know if I was well enough to come in.

But my therapist wouldn't charge me for being sick - I would think the therapist would have to take responsibility themselves for getting sick from clients if the policy is to charge them for canceling while sick, but maybe I'm just not understanding the logic of the policy!