I had tires mounted at Pep Boys because they were open late. One tire, the bead didn't seat properly, it went flat as soon as I hit a bump. Never going back

Does the shimmy happen at all speeds? Or only at certain speeds? Does it get worse with increased speed?

Do you hear any unusual noises (aside from the noise from the shimmy)? Especially when turning or going over bumps?

If no noises, or if you don't feel the steering wheel move a lot when you go over bumps, it's unlikely to be a control arm or other suspension link. And if you don't feel the shimmy get worse (harder) when you brake, it's unlikely to be the tires, because braking---transitioning the weight to the front tires---would almost certainly cause that if it were the tires.