Early days horns made with rubber bellows connected to horn.by pressing(blowing air )air will make noise while passing through horn shaped funnel.this is why "blow horn".
In English usage "sound your horn" refers to your use of a vehicle's horn [attention-getter]".
Over time "blow your horn", which originally had essentially the same meaning, has been expanded to include the idea of advertising yourself and your attributes in order to gain the attention of others - so you have a Frank Sinatra song, "Come Blow Your Horn" from a Neil Simon movie of the same name, and much usage among people who are trying to persuade the shyer ones among us to take credit for their achievements.
Furthermore, when you say "sound your horn" you do not differentiate between vocal cords or a mechanical device whereas "blow" actually refers to your physical action in making the horn resound. Hope this helps.