Hypertensive Emergency: Given the patient's significantly elevated blood pressure (170/120 mmHg) along with symptoms such as giddiness, muscle cramps, and shortness of breath, a hypertensive emergency is the most likely diagnosis. Hypertensive emergencies are characterized by severely elevated blood pressure with evidence of target organ damage, which can include the brain (causing dizziness or giddiness), heart (leading to symptoms like shortness of breath), and kidneys (potentially causing muscle cramps due to electrolyte imbalances).

Preeclampsia: Although less likely given the age and no mention of pregnancy, preeclampsia is a condition characterized by new-onset hypertension and often proteinuria after 20 weeks of gestation. It can cause symptoms similar to those presented, including shortness of breath and potentially muscle cramps.
Chronic Kidney Disease (CKD): CKD can lead to hypertension and electrolyte imbalances, which might cause muscle cramps. Shortness of breath could be related to fluid overload or anemia associated with CKD.
Hyperaldosteronism: A condition where the adrenal glands produce too much aldosterone, leading to high blood pressure and potentially muscle cramps due to hypokalemia (low potassium levels).

Pulmonary Embolism (PE): Although the primary complaint is hypertension, shortness of breath is a key symptom that could indicate a pulmonary embolism, a potentially life-threatening condition that requires immediate diagnosis and treatment.
Cardiac Ischemia/Myocardial Infarction: The combination of high blood pressure and shortness of breath could also suggest cardiac ischemia or myocardial infarction, especially in the context of obesity, which is a risk factor for cardiovascular disease.
Aortic Dissection: A severe and life-threatening condition that can present with high blood pressure and could potentially cause shortness of breath or giddiness due to compromised blood flow.

Phaeochromocytoma: A rare tumor of the adrenal gland that can cause episodes of high blood pressure, along with symptoms like palpitations, sweating, and headache. While less likely, it's a diagnosis that should be considered in cases of resistant or episodic hypertension.
Cushing's Syndrome: A rare endocrine disorder caused by excess cortisol, which can lead to high blood pressure, among other symptoms. Muscle weakness could be a presenting symptom, potentially misinterpreted as muscle cramps.
Hyperparathyroidism: Can lead to hypercalcemia, which might cause muscle cramps and weakness, and is associated with hypertension, though it's a less direct connection to the patient's primary complaints.