If I really trust Hashem, why do I still feel anxious?

Rabbi Landau answers that your fear is not a sin. The mistake is thinking that bitachon means feeling calm. “Calmness is a personality. Bitachon is a choice.”

Even Dovid HaMelech said, “Libi chalal bekirbi,” my heart trembles within me. He felt the fear, and in that same moment he sang Tehillim.

The pasuk says, “Hashlech al Hashem yehavcha,” throw your burden on Hashem. Rabbi Landau points out that it doesn't say you won't feel the burden. “It says you don't have to carry it alone.”

So bitachon “isn't the absence of fear. It's the courage to say, ‘Hashem, I trust You,’ even while I'm shaking.” And it is a choice you make constantly, again and again, inside the fear itself.

Also answered in this teaching

Did Dovid HaMelech ever feel afraid?

Rabbi Landau notes that Dovid HaMelech said “Libi chalal bekirbi,” my heart trembles within me, and in the same moment he sang Tehillim.

Going deeper: Rabbi Landau's teaching, level by level

Surface claim

Feeling fear does not mean your trust in Hashem is fake. Fear is not a sin.

Fear, vulnerability, or tension

People blame themselves: if I really trusted Hashem, I wouldn't be anxious.

What may be behind it

The confusion is between calm and trust. In A Soul at Peace, Rabbi Landau writes that calm is a character trait, nothing to praise and nothing to be ashamed of, while trust is a choice.

Deepest human truth

The verse says to throw your burden, which means the burden is felt. In A Soul at Peace he writes that you first have to admit the weight is there; only then can you throw it on Hashem and not carry it alone.