This building really need some basic renovation, outside fassade and and inside ventilation systems.
Unfortunately there is no fast solution to the entire set of problems exept of finding a better place in Gdansk or surroundings.
I hope your visa will come soon. If you move it maybe can redirected to your new place you hopefully will find.
Anyway I would start searching a new appartement and stay outside in fresh air, as often as possible.
This maybe can have a nice side effect:
Ross' videos of Gdansk, polish supermarkets and DIY shops
Just a weird idea.