Get some good lopping shears, good gloves, and take the sucker out at ground level. Also clip out any broken or dead branches.

The rest can wait until spring. You can read up on how to prune citrus this winter.

yeah I'd get rid of the sucker, that can go anytime. everything else can wait until spring. Pruning tends to stimulate fresh growth and you don't want nice baby branches right before the cold comes. halfway through Feb I'd say might be a good time to give it a good pruning

You can search for local arborists or tree care professionals at the link below. Just scroll to the bottom of the home page and select your city or county. Any certifications that the individuals hold will be listed like certified arborist, certified tree care worker, consulitng arborist, etc.

Good luck

Here is a link that might be useful: Find a Tree Professional