The first time my chickens molted it freaked me out. I had one that was almost naked beak to toes. Then I had others that only lost a few feathers and still others that lost in patches that completely fell off in one area and when those were growing back, they lost feathers in other areas. Still I have some 2 year olds that have not molted yet, or if they did it was not noticeable. I have also had some of my summer babies molt the following fall. Each molt was different and they all molted at different times. They can molt at any time, although most prevalent in the late summer/fall and usually between 16-18 months. But it can happen sooner. Shorter days trigger the molting process.
Your feed is "Scratch and Peck" Layer pellets, 16% protein? If so, that is the bare minimum for healthy birds (it is commercial "industry standard" - they have determined the minimum amount of protein needed by birds used to mass product to get the most production at the lowest costs - 16% is where they landed). It works, it is just not optimal.
Most birds can benefit from a higher level of protein and if you have a rooster, he NEEDS, a higher level of protein. He can also get internal organ damage from the higher level of calcium in layer feed.
I feed mine a 20% all flock feed. Then I don't have to worry about getting more protein into them (via less nutritious treats) when they need it, i.e., at times of molting. I also don't have to worry about my rooster getting the additional protein he needs or too much calcium that he doesn't need. I feed them back their eggs shells as a treat (rooster is not interested in them) and give them free choice flaked oyster shells. They know when to eat more calcium. I don't do grit b/c my chickens free range all day at their leisure and can pick up grit from around the land.
Just some thoughts. Hope yous gal gets better quickly!