Fludrocortisone and Midodrine are both medications that can help raise blood pressure. Ask your physician if one of these medications would be right for your situation. People are not generally prescribed medicine for low blood pressure, as it's not often a cause for concern unless it presents with symptoms.
Why do the middle fingers lock up when experiencing pain in neck and shoulders?   One cause could be some kind of impingement (pressure or swelling that applies pressure) of the spinal cord at C7, one of the cervical segments of your spine.
The MCP joints of the fingers may actually begin to point sideways (towards the little finger). This is called ulnar drift. Ulnar drift can cause weakness and pain, making it difficult to use your hand for daily activities. Both rheumatoid arthritis and osteoarthritis can affect the IP joints of the fingers. The IP joints may begin to flex (bend) or hyperextend (over straighten), causing characteristic finger deformities.