I've had thoughts like that too, but I never knew there was a name for it. My thoughts usually are, what is the meaning of life? what is this life for? is there a purpose for everything we go through in our lives? But, I always seem to come up with answers to my own questions. Don't know if you have a certain faith, but I'm a Christian believer and I think having faith is what helps me find my answers.
I'm not sure if I answered your question----I have to admit, I'm not sure what existential anxiety is....I'll have to read up on it :)