I pretty much never buy anything with acrylic, which seems to be the most likely to pill, regardless of the item's price or apparent "quality." It's not the only offender, just the worst (in my experience).
When washing sweaters, I put them inside out and then zip them in a couple of lingerie bags. When needed, the sweater shavers are great (but TIME consuming!).
As for your shirts, I'm guessing they are a blend with some polyester...another pilling offender (though some poly blends are great!). Pilling isn't just something that happens in the washing machine. It's more likely that it is happening while you are wearing the garment, which is why you tend to see pills where there is naturally friction, such as the underarm area. That why I try to avoid fabrics that I know will break my heart later...
I enjoy shopping at thrift stores, which is a great way to learn more about which fabrics to avoid. Whenever I see items that have a new style but look thrashed, I take note!
By the way, did you buy the items recently? I don't know about ATL's return policy, but maybe they would provide replacements for you.
