Most certainly not. Perhaps squeezing would create more pain than simply walking around, but pregnant women can experience soreness in their breasts just lying on the couch.
Here are some tips to help with any soreness you may have:
Make sure you have a bra that supports you well, and make sure you have one that fits properly, during pregnancy breasts will grow and the last thing you want is a bra that is too small.
Avoid squeezing them or handling them in any kind of rough way. It may not be the only reason for breast soreness, but it is a reason.
You can also wear a bra while you sleep, it may be a bit uncomfortable, but if you find that you cannot sleep due to breast pain, the bra may help.
