not a good fit for the crown- gumline problem

Hello,
I had a crown placed a few weeks ago to cap my tooth,  with no root treatment. When the impression was being made the tooth was hurting and because of that I had been avoiding touching it too much with the toothbrush for a month before, so the gum was inflamed and puffy. After the crown placement I started brushing normally and the gum receded. Now I have a slit between the crown and the gum, where the crown doesn't reach, and a part of the tooth (root?) exposed along the gumline. It's very sensitive to temperatures and sweets, hurts when brushing, and food gets stuck in it.
Should I have the crown removed and replaced, or is there a way to leave it but solve the problem by, for example, putting a filling underneath?
If the dentist suggests the crown should be redone, should I pay for it again or it's the dentist's responsibility because he didn't think about the gum changing size after healing?
I would really appreciate any advice... thank you

[patriciat]

You really need to contact your dentist and make them aware of this problem.

Give them a chance to resolve this first.