Don’t panic.
I work with the stuff every day and have done for 13 years. As a surveyor I know what the stuff looks like and can spot it a mile off – and this makes me realise just how many times non-surveying people get exposed in a lifetime and don’t realise it. Every single week I see asbestos situations that are causing people’s exposure. However, when you consider just how much we would have been exposed as children in the 20th Century, these things are often minor. That’s not to say we shouldn’t minimise our exposure as far as possible. However, that one exposure is probably low compared to the amount you breathed in at your school back in the day, the amount that was being realised on poorly controlled demolitions, in housing stock, in the hospitals you visited, on the first jobs you did as a youth or in the offices we worked. I don’t know how old you are?
I often explain it as being a little like smoking. In theory, one cigarette can kill you, as that one cigarette could be the one with the benzene ring than binds to your DNA and causes the genetic change. BUT, it is dose dependant and the higher the exposure, the higher the risk.
The sore throat is not related, other than possibly psychosomatic or an issue caused by general dust release including the blockwork. Asbestos related disease doesn’t work like that. It sounds like you could do with some asbestos awareness training and I would recommend looking into it, even if it’s just a basic online course. It may ease your mind a little.
The only thing I would question is what has happened to the dust/debris you released by the drilling? Was it considerable and is it worth paying for a suitably trained contractor to do a localised clean with a HEPA vac (a vacuum with a filter that contains the fibres, not just breaks them down and spits them back out like a normal vac) to remove any remaining free fibres caused by the drilling?