Skepticism is indeed healthy, but beware of selective skepticism. Humans have a tendency trust people that they like or who make them feel good about themselves, and distrust people they don't like or who challenge assumptions they'd rather hold onto. So yes you should be skeptical, but you do need to keep yourself grounded.

How are you to convince a flat-Earther that the world is round? You can show photos of Earth taken from the moon, but clearly you have to trust NASA. You can show global flight traffic patterns that only make sense if the Earth is a sphere, but then you have to trust the FAA or wherever you're getting the airline data. You can dig up whatever evidence you want but at some point you'll need them to relinquish their skepticism and accept that these institutions are not part of a vast conspiracy to hide the shape of the Earth. Now apply that to vaccines, climate change, election results, economic theory and everything else that matters.

Institutions are imperfect. They have their own agendas and sometimes they happen to be wrong, and sometimes they flat out lie. If you only trust people that you like, you're liable to fall prey to charismatic charlatans. If you demand absolute certainty, you'll never get past a bedrock reality of cogito ergo sum. You have to make some sort of reasonable balance between trust and skepticism and accept that sometimes you'll be wrong.