Bo, I just hit the 60 year mark myself and for the last few years have really been disappointed at how easy it is to get injured and how long it takes these old bodies to heal.
First, assess how sore your shoulders are. You can probably feel if it's to the point of injury or just a little lactic acid buildup from working muscles in a new way.
If its just a little exercise soreness and not injury, ice and advil will take care of it. Strengthen the muscles with the various rotator cuff exercises. They are easy to find on the internet.
From the little I know of G.Fred's methods, the posture he teaches may be a little more condusive to shoulder stress. Straighten up and get your bow shoulder down & back. Relax your shoulder & neck muscles during the shot and rely as much on bone-to-bone support as possible. At full draw, you should be holding the weight with only your back muscles. Relax your shoulder tops, neck and biceps.
Since you haven't been shooting long, it would probably be a good idea to drop to about a lighter draw weight bow, in the 30 pound range. You should be working on your form at this stage of your shooting and a lighter bow is better for that.
Even though it's too much fun to quit after just a few arrows, you should gradually build up to a high volume of arrows. There really is no other activity that prepares our muscles for shooting a bow, so only shooting will build up the necessary muscles. As with any strength building exercise, you have to allow time for the muscles to rest before exercising them again. Unfortunately, this just takes longer than it did a few decades ago.
However, if there is the slightest doubt that it's anything more than exercise soreness, go see a doctor that specializes in shoulders. This is important because damage now could result in years of pain.
Good luck,
Allen