Well, this isn't something you're going to be able to hide, unfortunately for you. As soon as someone sees them they're going to know.

But, I think you're underestimating how understanding people can be. Your partner/friends might not even bring it up when you first show them your scars, and even if they do all you have to say is basically what you've said here; You were once severely depressed and anxious, but have sought treatment and are better now. Simple as that, and of course you could go into more detail if you wish.

You could also talk to a dermatologist about scar treatment, if they really bother you.