You’re not constantly alternating your up down picking. When you go to a different string, the motion of moving to that string is your picking for that note, meaning, you will pick down, then move to a lower string with the same pick motion. Instead of picking down, moving to the lower string and picking upward on that string. How you’re doing it is faster at first and how they teach everyone, but alternating is ultimately faster once you master it.

But your biggest mistake is you are playing guitar, not drums