Tendon/ligament take a long time to heal, if you decide to heal this through your own means, do your very best not to cause any stress in that region, the slightest damage will further prolong it's heal rate significantly. The reason for this is because of the type of tissue ligaments are made out of, they get very little blood supply, which means very little nutrients and oxygen flowing (oxygen is very important to healing). Assuming the damage was extensive, I don't mean that you should take it easy for a few weeks, a few months is probably more appropriate.
If you want to make sure that your ligament heals properly, or if you injure it again and are concerned about scar tissue building up, the best option is to go to a Physical Therapist. If you have health insurance, see what physical therapists will accept it, or go to your doctor and have him/her recommend who is best to go to.
Trust me on this, ligament/tendon injuries are not something you want to take lightly. It is said, and true, that it is better off that you break bones (have far better blood supply), before spraining ligament/tendons.
Being hunched over the computer for significant amount of time can and probably will lead to extensive cervical lordosis(neck elongated forward) and or thoracic kyphosis (hunched mid back), which is poor posture for your spine, and the hunched shoulders will lead to gradual tightening of the chest muscles.
I personally recommend going to a P.T. even if it turns out to be bull, make sure that it healed the "proper" way, and then start your own regiment of light stretches and exercises to prevent this from happening in the future.