I've had a sore throat for a week but no other symptoms. Could this be tonsillitis?

Not that I know of. If it's tonsillitis there will usually be more symptoms. Such as fever and difficulty in swallowing. I have had tonsillitis a couple of times. I was unable to swallow anything even drinking water hurt. However it was also because my tonsillitis were inflamed. Drink more water and look out for more symptoms.