It sounds like you are talking about tremolo picking. Without seeing your technique, it is difficult to give precise advice, but here are some pointers.
Keep a relaxed picking hand, and strive for consistency in your technique. Practice slowly, and use a metronome. It may seem boring, but practice with the metronome set to a tempo that is slow enough that you can execute smoothly, consistently, and without mistakes; then increase the tempo a bit. Continue this over a period of weeks until your tempo is acceptable.
Pay particular attention to mechanics when you switch strings, and be consistent in how you approach this. If you stick with strict alternate picking, you will follow a downstroke on the first string with an upstroke on the next string, and vice versa. But you may also choose to follow a downstroke on, say the sixth string, with another downstroke on the fifth string. This technique can save motion; sometimes it is called economy picking, and I find this more useful if you pick more from your elbow than from your wrist.
You may benefit from some simple exercises that you can make up to focus on particular problems. For example, just play one note on one string, tremolo picking with a metronome. Or alternate between two notes on the same string while tremolo picking. Or alternate between two notes on adjacent strings while tremolo picking. You don't need to spend a huge amount of time doing exercises like this; just make them a part of your daily practice, do them for 10 or 15 minutes maybe, but do them right and really focus to get the best results. And seriously, use a metronome.
As for trouble with higher strings, I don't know exactly what the trouble is here, but I would suspect that it is a control issue that will be improved through practice as suggested above, with an emphasis on consistency, control, and accurate tempo. Of course, as with any technique, be sure to practice everywhere on the neck, especially in places that give you problems.