The biggest telltale sign that a pig has mites (burrowing/mange mites, rather than ear mites) is the constant scratching! They'll be very itchy and their hair will often be thinning in places or breaking off partway down the hair shaft.
Mite treatment is usually Ivermectin; administered either as a 'spot on' drops type treatment (like Xeno 50 or Xeno 450, depending on age) OR some Vets give ivermectin by injection instead.
As with anything, obviously it's important to be sure of what you're dealing with before you look at treatment, especially as fungal skin infections are also very common in pigs and can also cause pigs to bite and/or become very agitated when touched, so that's also definitely worth bearing in mind too!
Gorgeous Guineas has lots of useful info about piggy skin issues:
http://www.gorgeousguineas.com/indentification.html
http://www.gorgeousguineas.com/parasitic.html
Hopefully Saffy's just nervous and will settle down soon but in the meantime I'd keep an eye on her skin/body in case it's something else which is troubling her.