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 swelling makes it difficult for the affected tendon to slide through its membrane (tendon sheath), causing the pain and stiffness associated with trigger finger. The swelling can cause a section of the tendon to become bunched into a small lump (nodule) at the base of the affected finger or thumb. If a nodule forms, the tendon can get trapped in the tendon sheath, causing the affected finger or thumb to become temporarily stuck in a bent position.