Reading out loud in general is useful. If you're already pretty fluent by yourself, it means the nerves are simply getting to you when other people are around. That's something very common as public speaking is the most common fear out there. You're experiencing the same fear as everyone, yours just expresses itself through your stutter. The solution to fear? Exposition! The more you do it, the lesser it will impact your speech. You're lucky to have people that are willing and patient about your speech when you speak in front of them, you can cherish that very much! Keep doing what you're doing!