Pain/swollen vein in right calf for 2 weeks, shortness of breath and small cough for 1 day, risk of DVT. Could I have a pulmonary embolism?

Possible. I would see your primary care doctor as soon as possible, especially if shortness of breath persists. They will be able to determine. This might even be an instance to go to the ER. It is difficult to determine based on the evidence in the question.

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