I know 3 guys that are shorter than me. I'm just 163 cm (5'3). Guys come in all sizes. These guys have had the same problems as you. They have not been taken seriously and not their age.
I count as a short guy, but if you show confidence and feel one with yourself, others will pick that up and treat you like a grown up. If you are uneasy or uncomfortable people will pick that up and act on that.
People are people. They act on gut feeling. If you look nervous in a store, they might think of you as a shoplifter or that something else is wrong. I know, I do the same.
Confidence can come with age, it did for me. You can also act confident.