Congestive Heart Failure (CHF): This is the most likely diagnosis given the patient's symptoms of worsening shortness of breath and bilateral low leg edema, which are classic signs of fluid overload, a hallmark of CHF. The absence of fever, cough, chest pain, and palpitations also points towards CHF as these symptoms are more commonly associated with other conditions like infections or acute coronary syndromes.

Chronic Kidney Disease (CKD) or Nephrotic Syndrome: These conditions can lead to fluid retention and edema. Although less likely than CHF given the presentation, they are plausible, especially if the patient has a history of kidney disease or diabetes.
Liver Cirrhosis: Cirrhosis can cause fluid retention leading to edema, particularly in the lower limbs, due to hypoalbuminemia and portal hypertension. However, other signs like jaundice, ascites, or a history of liver disease would typically accompany cirrhosis.
Deep Vein Thrombosis (DVT): While DVT can cause unilateral leg edema, it's less likely to cause bilateral edema without other symptoms like pain or warmth in the affected limbs. However, it's a consideration, especially in immobile patients.

Pulmonary Embolism (PE): Although the patient does not have typical symptoms like chest pain or cough, PE can present atypically, especially in the elderly, with only shortness of breath. Missing PE can be fatal, so it must be considered.
Cardiac Tamponade: This is a life-threatening condition that can cause shortness of breath and, less commonly, peripheral edema due to impaired cardiac filling. It's crucial to consider, especially if there's a history of trauma, cancer, or pericarditis.
Constrictive Pericarditis: This condition can mimic CHF with symptoms of fluid overload but is less common. It's essential to consider in patients with a history of pericarditis or cardiac surgery.

Lymphedema: This condition can cause chronic swelling of the limbs but typically presents unilaterally and is less likely to cause shortness of breath.
Superior Vena Cava Syndrome: This rare condition can cause edema of the upper body due to obstruction of the superior vena cava but would not typically cause bilateral lower limb edema.
Idiopathic Edema: Also known as cyclical edema, this condition can cause intermittent edema without an identifiable cause, but it's less likely to cause significant shortness of breath.

History and Physical Examination: A detailed history focusing on cardiovascular, renal, and hepatic diseases, and a thorough physical examination to assess for signs of fluid overload, cardiac dysfunction, and other systemic diseases.
Laboratory Tests: Basic tests including complete blood count, electrolytes, renal function tests, liver function tests, and cardiac biomarkers (e.g., BNP or NT-proBNP) to evaluate for CHF and other conditions.
Imaging Studies: Chest X-ray to evaluate for cardiomegaly or pulmonary edema, and lower limb Doppler studies if DVT is suspected. Echocardiography is crucial for assessing cardiac function and structure.
Other Diagnostic Tests: Depending on the suspicion of other diagnoses, further tests like abdominal ultrasound for liver disease, or CT scans for PE or other conditions may be necessary.

This approach will help narrow down the differential diagnosis and guide appropriate management.