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Well, it could be a number of things.
If there is actual swelling in the lower leg, there is the possibility of a blood clot causing symptoms.
If you have recently been strenuously exercising, there is the possibility of the calf muscle itself being strained, or the tendons being inflammed.
Pain down the back of the calf itself could also be a symptom of nerve related issues, such as "sciatica", though the pain often also involves the buttock and the back of the thigh when this occurs.
So there are a few possibilities, and seeing your doctor for an exam can help to narrow this down.
What type of doctor should I see for this type of pain?
I would start with your primary care doctor.
Then depending on the exam, they can order the appropriate testing, which may be an ultrasound of the lower leg, or an xray, or a MRI of the lumbar spine, or referral to the appropriate specialist, which may be a orthopedic surgeon.