I'm going to assume it was only a grade 1 separation. As you can see from the picture here, a grade 2 separation has significant ligament damage associated, and you should probably wait about 2 months before using your shoulder regularly again. A grade 3 separation would require surgery to reattach.
There are a few other types, but they are of the very rare variety.
I second others in saying that rest and rehabilitative exercise are your best option, so a physiotherapist is your best bet. Have your diagnosing physician refer you to someone.
One thing that probably wasn't mentioned: white connective tissue takes an exceptionally long time to heal, so don't do too much vigorous activity with that shoulder until the 2 month mark (8 weeks). If you haven't aggravated it during that time, you should heal with a perfectly stable shoulder. If you put too much strain on your shoulder (particularly with carrying heavy weights) the scar tissue may tear/stretch, and you may heal with the ligament in an elongated position, resulting in shoulder instability. That would be worse long term, so be patient right now while you're healing up.
Swimming makes sense to me, but don't be too vigorous for the first few weeks. If you have a flare up of pain/inflammation following the activity, you probably need to back off on the intensity. That's where the anti-inflammatory creams/pills will cover up important symptoms that you need to pay attention to.
Any other questions, don't hesitate to ask.