Yes. "I feel better knowing that" means "that information calms me or relieves my stress" Examples: There was a lot of vocabulary on the test, but I feel better knowing that I studied. My grandma passed away recently, but I feel better knowing that she is in a better place and is no longer in pain.

This means that someone feels more positive about a situation because of having some piece of knowledge. For example, I feel better knowing that my grandfather had a lot of family around him when he died. If I didn't know this, it would add more sadness to the situation.

"I'm being relieved" is not appropriate there. That means "someone else is going to do my job". Just say "I am relieved".