new drywall adjacent to existing wall
It's going to be very difficult to get a good finish using drywall compound slathered on thickly.
I recommend that you remove the drywall you installed and re-frame or shim the doorframe out so that once you place the drywall it will be right in line with the existing drywall.
That should leave you with just a seam to be taped and make finishing it much simpler.