I looked out the window and they're all grazing in their usual group and nobody has gone off alone to sulk.
As an inexperienced caretaker, it's odds-on you are being over-worried. Most of us do (or did)!
However... sick sheep often do not show signs of being unwell until they are in a bad way. Because they are a prey species, and predators will pick off the weak and infirm, so it's a survival thing to behave like all the other sheep in the flock as long as you are physically able. Hence the saying that often the first sign of a sick sheep is a dead sheep.
I think you've said that these sheep are just lawnmowers? So not pregnant? Therefore they'll be able to handle a bit of exercise...

I'd be inclined to move them about a bit, not running scared but just get them moving away from you at a trot, round the paddock a few times, until there's a bit of heavy breathing. Then watch how they recover. If the potentially ill one recovers as well as the others, then I'd say you should be okay to wait for the farmer who's visiting tomorrow. If she heaves, rattles, sneezes and snots longer than the others, then it could be something infectious developing...
I've no experience of nasal bots so can't comment on that possibility.
If you did get them penned up, get the one you want to catch moving along the wall then catch it by using your right arm to shoo them forwards into your left hand, left hand under chin. (Or left/right reversed, whatever feels comfortable to you.) Then bring your body up to the flank and using your knees, one near the shoulder and one nearer the rear, with your hands under chin and on the tail head, pin them against the wall, and manoeuvre them with their bottom into a corner so you can use one hand to look at eyelids or whatever.
Try not to grab handfuls of fleece, as it does bruise - but better to do that briefly and then secure them using your body, than to let them learn they can wriggle out of your grasp!

(Note that these catching instructions are assuming we are talking little wiry Hebrideans. Different tactics would apply for heavyweights such as Suffolks, Texels, etc.

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