My oldest and youngest both can get 85% of any childproof thing open....Pill bottles or whatever else.
We have had to have all things dangerous behind a padlocked cabinet since my oldest slept walked into the kitchen one night and grabbed three knife while climbing onto of counter...most scary moment up until my youngest started moving....
We are having to drill a place to lock lock our fridge now too because of my two Houdini's. We have tried every type of none permanent locks....They figure everyone of them out!
As for the teething tablets, they are pretty harmless. I would give milk and just keep an eye to kiddo.
My kids have ingested everything from the silicone moisture packets they put in shoes boxes to almost a whole tube of sunscreen...
Always call Poison Control to make sure.
they are so sneaky when they want to be!!!