the possible causes of your problem could be,
-as the baby grows it will push the diaphragm upwards which will lead to difficulty in breathing.
-around the time of delivery breast will be containing milk which may be the cause of heaviness in chest.
-there will be increased blood circulation during pregnancy
putting more pressure on heart that may be responsible for squeezing sensation.
all these are normally seen in term pregnancy,
if you are feeling trouble with these better to consult the doctor and get examined.