You can use the adjective leery to describe someone who's suspicious of a person or situation. After his brother came out with bald spots and uneven patches of buzz-cut hair, he was leery of having the same barber get near his own head.
Being leery is being distrustful. If you're leery, it will probably show on your face and in your posture. You may squint and wrinkle your brows or take a few steps back. If you're leery that someone won't keep a secret, you won't confide in them, and if you're leery about whether they'll keep a promise to you, you won't count on them. Sometimes people are leery because of some proof, but often, just having a bad feeling or instinct is enough to make a person leery.