Lights

Hi, my tag lights went out so I replaced
them. When I took everything apart and got
to the bulbs I found that the driver side bulb
had began melting the white piece it sits in. I
figured I'd still replace the bulbs and
address that on a later date. When I put the
driver side bulb in it lit right up. Then when I
put the passenger side bulb in not only did
the driver side tag light go out but so did my
running lights in the front and back on the
driver side only. The high/low beams work
along with the blinkers, hazards, brakes, and
reverse lights. So now my plate lights still
don't work but I'm now having this New
issue. I'm at a lost. I've checked fuses and
bulbs for broken filaments and have found
nothing. Hope somebody has the solution.
Thanks.