Psychotic Depression: Given the patient's history of depression and current presentation of agitation, tachycardia, hypertension, and delusions (specifically, the delusion that she has no face, which is a somatic delusion), psychotic depression is a strong consideration. The presence of intellectual disability may complicate the diagnosis but does not rule out the possibility of psychotic depression.

Schizophrenia: Although the patient's age of onset might be considered late for a first diagnosis of schizophrenia, it's not unheard of, especially in individuals with intellectual disabilities who may have been misdiagnosed or whose symptoms were attributed to their intellectual disability. The delusion about having no face could be a part of a broader psychotic symptomatology.
Bipolar Disorder with Psychotic Features: If the patient has a history of manic or hypomanic episodes in addition to her depressive episodes, and considering her current agitation and delusional state, bipolar disorder with psychotic features should be considered.
Delusional Disorder: This diagnosis could be considered if the delusion about having no face is persistent and not part of a broader psychotic syndrome, and if the patient's functioning is not markedly impaired outside of the direct impact of the delusion.

Neuroleptic Malignant Syndrome (NMS): Although less likely without a clear history of recent neuroleptic use, NMS is a medical emergency that can present with agitation, tachycardia, hypertension, and altered mental status. It's crucial to consider this diagnosis due to its high mortality rate if untreated.
Serotonin Syndrome: Similar to NMS, serotonin syndrome is a potentially life-threatening condition that can occur with the use of serotonergic medications, which are commonly used to treat depression. Symptoms include agitation, tachycardia, hypertension, and can progress to more severe manifestations.
Thyroid Storm: Hyperthyroidism can cause agitation, tachycardia, hypertension, and delirium. Although less directly linked to the delusion, it's a condition that requires immediate medical attention.

Cotard's Syndrome: A rare neuropsychiatric disorder in which a person believes they are dead or do not exist. While the patient's delusion about having no face might not perfectly align with Cotard's syndrome, it's a rare condition that could be considered in the differential diagnosis of delusional disorders.
Charles Bonnet Syndrome: Typically associated with visual hallucinations in visually impaired individuals, it's less likely given the description but could be considered if the patient has a history of visual impairment and the delusion is part of a broader hallucinatory experience.