I wouldn't normally push the head back in unless I have
only the head.
If I've got one front leg and the head I will have a feel to see if I can easily and safely get the other front leg, and if I can't, I'll usually deliver it with one front leg, as you did.
I would trace back up to the shoulder to make absolutely certain it's the leg of the same lamb, then feel my way across the shoulders and find the other front leg. By then I should have an impression of the width of the lamb's shoulders and of her birth canal, and know whether I really need the other leg forward - sometimes if it's a highly-muscled type of lamb and the mother's birth canal is a bit narrow, the backward-facing shoulder can be too much for her. But generally, unless you are breeding extreme fat lambs, she should cope.
If I didn't feel confident to pull the lamb forward with only one leg, and I can't safely get the other, then I would get the vet. They can give her something to stop her pushing, which makes getting the other leg very much easier
Don't beat yourself up - you have a live lamb that's suckled
Another time, if you can see the muzzle or tongue, you should be able to see two feet. If you can't see two feet alongside the muzzle, then yes, get in there. Give her maybe 10 or 20 minutes if you like, in case it's coming slightly lopsided, but if you still only see one foot, get in and have a look.
It's right to want to leave our girls to do the job naturally, and I know a lot of us old hands do go on about some people intervening too soon. But... so long as you use plenty of lube, give her antibiotics if you've been inside, make sure your fingernails are short and smooth, your hands clean, and you don't do anything rough in there, you won't harm the ewe by having a look.
And if everything is coming right, then you can leave her to get on with it at her own pace
Don't ever hesitate to call the vet in if you aren't sure how to proceed. BH still gets the vet for some difficult ones, and he's been lambing 200-400 ewes a year for 45 years
It's one of the things I admire about him - he'd never risk the ewe or the lambs by struggling on himself if he can't work it out or get them to come right.