Ashamed and disgusted

My husband and I have been together for 10 years. I’ve suffered from depression for most of those years but I finally came out of it at some point last year. I realized a big part of the depression came from being unhappy with my relationship. A big issue is my husband’s hygiene and appearance. It’s awful. He’s a mechanic so he’s always dirty. It’s like I have to beg him to shower and sometimes he still won’t for a few days. He stopped brushing his teeth at some point a LONG time ago. He won’t even use any kind of face washes to help with acne. He also won’t go to see a doctor. At first I thought he was going through depression too but now I just think he’s nasty. Then he wonders why I don’t want to go anything sexual or show any affection. I love him with all my heart but most days I’m ashamed of him. I refuse to even introduce him to people who come around. Like I just literally pretend he’s not right there and pray no one else looks at him at all. It’s messed up I know, but I don’t know what else to do. He also lies about pointless things and he never keeps his promises. When I try to talk to him about any of the bad things he’s doing, his feelings get all hurt and he apologizes and tries to make up to me. But at this point I think he’s faking it. I dont believe he feels bad about anything he does, he just wants me to shut up. I don’t want to leave but I can’t live the rest of my life like this either. Any advise?