Etienne,
sounds like you have stressful work to start with, and maybe facing the new added responsibilities of fatherhood, has just pushed you to the point of suffering from the degree of stress, including the raised BP and the muscle spasms. A GP could help, to start with, to assess the extent to which the raised BP is a chronic and severe level needing treatment in it's own right, or whether it, like the muscle spasms, might respond to a mild sedative tranquilizer for a few weeks. And yes, getting more exercise is not merely healthy in its own right, but often helps us to handle stress better.
Most people recognize that pregnancy and childbirth, etc., are obviously stressful for the woman ; they forget that it can be pretty stressful for the man, as well. Especially because something so important in his life is happening, without any refined role for him to play.