Could it be possible that a new crown was too large and cracked the tooth behind it? (Photo)

It is extremely unlikely that your new crown fractured the adjacent tooth. A new crown almost always has a feeling of being "tight" when it is first cemented. That feeling generally goes away almost immediately after cementing the new crown. The cracks in your back tooth were more than likely caused by biting forces on a tooth with a worn out silver filling.I recommend you have that back tooth fixed ASAP to avoid further complications; like a root canal.Good luck!

Most likely the tooth always had a fracture line, it is very improbable that the new crown caused the fracture

More than likely, the existing filling is what cracked your tooth. Just bad timing. Silver/Mercury fillings weaken teeth by up to 85% and expand and contract in response to heat and cold like an old Mercury thermometer. Those of us who don't do them call those fillings temporary crowns because eventually that tooth will need a crown.