I've been through it a few years back with health anxiety and I'm still on medication to help keep an even keel. I was/am open with my doc and FEO and at no stage has there been talk of removing my guns. Infact my FEO was incredibly understanding and supportive saying that removing my guns could make it worse as shooting is a great way to get out, meet people and improve state of mind....and she was right.
As has been said, go talk to your Doc and do it as soon as you can.
I'll offer up some advise, you'll get help but the person who can help you the most is yourself, challenge your thoughts challenge the lethargy, when you're down... get up, grab the gun and the dog and get out in the sunshine, walk hard, watch your dog enjoying itself, marvel at the sky, take in nature.....you will feel better for it.
It may surprise some that I'm so open on a forum but I'm a firm believer that openly talking about these things is the way forward. Its not something we should shy away from.
Get some help but remember to help yourself! hope you feel better soon.