Mechanical things like hayseeds, maggots and the like can cause noses to run. As can orf virus (blisters around the nose and mouth) and watery mouth (though as it sounds they drip at the mouth too and are poorly).
Don't know what else, as I've never had lambs have this. Don't think sheep get colds, ie upper respiratory viruses, like us, though I don't know why not. Mind you, neither do dogs.
I'm sure you shouldn't and no doubt I'll be told so, but if she were mine I'd give her a jag of penicillin.
And then if not less 'under the weather' soon talk to the vet.
And you're right, heptavac isn't really effective til a fortnight or so after the second jag.