Well done for saving her.
If the vet and farmer can’t diagnose from seeing the lamb, we are not going to be able to do it from a description! We probably won’t be able to do it from pictures either, but it would at least give us a fighting chance!
Which said, the nose lesion sounds like orf. And yes, if it is orf, she’s busy infecting your whole house, and yes it’s a zoonosis and you can catch it. And the virus can live a long time inside a house, on fabrics, etc. It gets in through broken skin, so if it’s there, it will get one of you when you have a cut, a blister, or something. At its least offensive it’s intensely irritating verging on painful, and rather unsightly. Takes about 6 weeks to clear up. At its worst, people have had it get into joints and been hospitalised.
The other thing which I thought about as I read your description is that some brands of lamb milk are irritating to skin, especially broken skin. Is it possible she has got milk over her face, and that has caused her wool loss? And if she had a cut on her nose from nosing at something sharp, and gets milk on that cut when she feeds, then it could keep the lesion from healing. How would you know if you have one of these types of milk? If one of you has a cut or a keen, spill some of her milk into it, and you will know.
In terms of finding her somewhere more appropriate to be, it might be impossible now she has possible orf, but any sheep farmer is likely to have batches of bottle lambs, so she could (if you can find a farmer willing) join one of her own age group. Look for a farm which has lambs the same size as her in their fields, and knock on their door
. Proper farmers will have enough to be able to batch the lambs in appropriate size / age groups, so she would have playmates her own size.