My youngest son's kindergarten teacher thought he was ADHD. After helping him with his difficulties with letters and numbers, I had his eyes checked and found out he had amblyopia. After vision therapy and patching, his ADHD symptoms disappeared. School testing did not place him in the gifted range, however, I think he still has his talents in art and music (he can learn and play the violin and piano by ear).

He is very shy and tends not to want to draw attention to himself so sometimes, I wonder if he holds back

Tests could possibly be administered incorrectly. Some districts conduct testing through their GT department instead of the classroom teacher. Perhaps you can try another test next year in a different setting.