Not normal. Congestion at night is not uncommon but if people experience significant pressure then it becomes more concerning. Headaches at night can be sinus related or it even be a sign of significant sleep apnea (but that is more consistent with morning headaches). For people with similar complaints, an ENT visit is warranted.
Sinusitis? Sounds like a sinus infection or sinus inflammation from allergies. See your doctor or an urgent care for evaluation and treatment.