Food is getting trapped between my dental crown and the next tooth, is this normal?

Food commonly gets stuck around our own teeth... even those that have never had any treatment.  That is why dental floss is so important.  Since you just had treatment done, it is premature to advise you conclusivly.  I would advise you to purchase a water pick, or a different type of floss that is thicker (like oral b tape floss)  and try that until the area fully heals.  If it seems to be an issue after 6 weeks, return to your doctor and ask if she can re-evaluate the contact between the crown and your own tooth.

See if the situation improves as often it does take a few weeks for things to feel normal. If the problem continues then suggest to your dentist to have the crown replaced with a new one.

It sounds as if your doctor is trying to avoid fixing a problem with the size of the crown that was placed. It is NOT normal to have a minimal gap, and the crown should create a contact similar to your other natural teeth.