Atrial Fibrillation with Rapid Ventricular Response (RVR) and Possible Pulmonary Congestion: The patient's high cardiac rate of 150s, shortness of breath, and low oxygen saturation of 87% in the context of atrial fibrillation suggest that the arrhythmia is not well-controlled, leading to decreased cardiac output and possible pulmonary congestion. The recent history of cough and colds could exacerbate this condition.

Pneumonia: Given the patient's recent history of cough and colds, pneumonia is a plausible diagnosis, especially considering the shortness of breath and low oxygen saturation. The presence of atrial fibrillation could further complicate the clinical picture.
Chronic Heart Failure Exacerbation: The patient's symptoms of shortness of breath and low oxygen saturation could indicate an exacerbation of heart failure, especially if the atrial fibrillation with RVR is not adequately managed.
Pulmonary Embolism: Although less likely given the absence of chest pain, pulmonary embolism remains a consideration, especially in the context of shortness of breath and low oxygen saturation. The patient's age and possible decreased mobility could increase the risk.

Cardiac Tamponade: Although less common, cardiac tamponade is a life-threatening condition that could present with shortness of breath and tachycardia. It's crucial to consider, especially if there's any suspicion of bleeding (e.g., from dabigatran) or if the patient's condition rapidly deteriorates.
Myocardial Infarction: Despite the denial of chest pain, myocardial infarction (MI) must be considered, especially in the context of atrial fibrillation and a rapid ventricular response. MI can sometimes present atypically, especially in the elderly.
Bleeding Complication from Dabigatran: Given the patient is on dabigatran, any sign of bleeding (which could be internal and not immediately apparent) is a critical diagnosis not to miss, as it could lead to severe consequences, including cardiac tamponade or significant blood loss.

Pulmonary Hypertension Crisis: This is a less common condition but could explain the shortness of breath and low oxygen saturation. It would be more likely if there were pre-existing conditions suggesting pulmonary hypertension.
Aortic Dissection: Although rare and typically presenting with severe chest pain, aortic dissection is a diagnosis that cannot be missed due to its high mortality rate. The absence of chest pain does not entirely rule out this condition, especially in the elderly, where presentations can be atypical.