I have an alternate suggestion, but you may not want to do this at first as it may actually interfere with your progress with more normal exercises (like the other fine answers here).
In addition to working on metered picking, there is also unmetered speed picking which is more like the tremolo technique used for melodies on the Mandolin.
Think Dick Dale's Pulp Fiction theme (I forget the real title) to get the idea, but don't copy his technique. He uses a great deal of force to achieve a distinctive sound. But using force this way is not a good idea for a beginner (or anybody, really).
Instead, for the best start, watch the old Humphrey Bogart movie To Have And Have Not (it's just as good as Casablanca, just less well known). Specifically, there's a scene with a Gypsy guitarist in the Café. The technique she uses is a very fast tremolo strum with the flats of her fingertips. Of course, the notes are not ringing since the vibration is constantly being stopped by another finger. Basically, each string of the chord is going through a very fast cycle of ring -> mute -> ring -> mute -> ring -> mute.
Practicing this finger-strum technique will help you work on the balance between the muscles of the wrist and forearm and higher-up in the shoulder as well. But the musical effect is not strictly about super-speed but fluidity and supporting a singer with a very free rubato, almost no time at all.
Next, grab the pick and try doing a tremolo on one string with heavy palm-muting. We want to stop as much ringing as possible with the muting so the string doesn't move around so much. This makes it easier for the pick to "find" the string in the reverse direction and should help avoid increasing the tension in the muscles. Use a thick string and fret it very high up the neck, too, to reduce the string's vibration further. I'd recommend a thick pick with a dull tip for this, too. It should have less drag than other kinds.
Next, try a mandolin-style tremolo melody, even just running scales will work. Now, we're deliberately not counting notes here. Up-and-down-and-up-and-...-down-and-up-and. Don't count in the middle, but pay attention to the very last stroke of one note and the start of the next. If you're changing frets on the same string, I think it works best to start the new note with a down-stroke. If you're switching strings, however, it's best to sweep into it. So, a down-sweep if you're going up a string (in pitch). And an up-sweep if you're going down a string (in pitch).
Next, try with different pick thicknesses/pointinesses. A thinner pick, a sharper pick. These will all drag differently, losing more or less energy to the string, requiring more or less muscular power/control to compensate.
So I'd recommend following the other, metered suggestions for a few months or even a year. Then, when you hit a plateau with that effort, come back and attack it from a different angle. Do this for a few weeks or months without doing the normal metered exercises. When you go back to them, you should find yourself back on the mountain again. :)