The likely cause of the swelling was gasses produced by bacteria, which may or may not be harmful. Better safe than sorry I think.
As for the date; without the swelling, I would have eaten it at one or two days over, but made very sure that it was thoroughly heated. Even if the supermarket and their suppliers are fully compliant with all the rules on temperature, and your fridge is keeping the contents below 39F there are still some unknowns. In particular, the journey between the store and your fridge. It’s also possible that the packaging was compromised in some way.
It may be worth buying a fridge thermometer and checking the internal temperature.
I throw out food well before the arbitrary ‘eat by’ date, and mainly avoid packaged foods that could spoil. It’s not worth taking a chance. With the kids gone it’s harder to shop for just the two of us though, the kids were massive consumers of leftovers, i didn’t need to work out how much of anything we’d consume in a short time, nothing lasted a long time.