The key to alternate picking, is to be able to start on a new string with an upstroke.
That will help your speed. It's different at first just make sure that you follow down up down up down up.
try this exercise.
G --------------------------11---12--11----------------
D----11---12---14---------------------------14----12----11----
and repeat. Start slow and work up.
Sometimes I hit notes only dogs can hear.
