Some really bad advice on this thread (though some good advice too!)
Firstly, Pegs are an absolute classic running shoe for a reason. They're now on their 37th model precisely because they're cushioned, supportive, neutral, and suit almost everybody. Personally, I wouldnt run in anything else on the roads now, after years of working through Hoka, Brooks, Asics and the rest. Pegs are just a very, very, good and versatile shoe for everything from short runs to marathons and above.
The "almost everybody" is key though. They won't suit absolutely everyone and there is a chance they're not right for you, OP. From all you've said, though, I suspect that's the wrong conclusion to immediately jump to.
It seems much more likely that running in a cushioned and supportive shoe for the first time is making you run "properly", after previously flat-footedly "slapping" the ground in your unsupportive shoes. That means your muscles will be having to adapt to firing properly, and it's not surprising they're complaining about that!
What's also exacerbating the situation, I suspect, is running in them every day. Even slight heel-toe drops take adapting to, so a massive change from old and flat shoes to a really decent shoe will be massive. You need to adapt slowly.
I would recommend breaking them in gently and building up slowly in the new shoes. Foam rolling will also help the muscle pain. Good luck!