Don't trust people too quickly, and don't expect others to trust you quickly, either. Trust is developed over a long period of time, and must be earned through the proving of your character in a variety of situations with someone.
It can be frustrating when you feel like you've done more than enough to earn someone's trust and yet they don't trust you as much as you think they should. Just be patient. Just give it time. Both your true character and their true character will gradually emerge as you continue to develop your relationship together.
Let your character speak for itself and you won't have to convince them that you're trustworthy.