Problems Picking

Firstly don't forget to relax - maybe before you start playing pause and visualize yourself striking the strings in a softer manner. (You may not need to do a down and an up strike all the time, it depends on the rhythm of the song you are playing or on what string you are going to hit after the preceding one.)
Just take as an exercise to do the down and up strokes evenly one after another, without bothering about a song, at first- just to get the up strokes happening, it just takes time and practice and it helps if you can have someone to show you.
It's natural that you will have difficulty at first because it's just new territory for your brain and muscle memory. I guess it's like when we learnt to walk as babies, we will always make mistakes at first. Hope this helps :)

Sounds to me like it's the angle of the pick. If you're angling the pick back (so the tip faces a bit upward) when you're picking down, you'll give a more resistance going back up.

Angling the pick like that isn't a bad thing - lots of pros do it. But they're also using just the very tip of the pick, and they've developed a lot of control. For beginners, I recomment having the pick flat (completely perpedicular to the strings) for single notes until you get the feel of picking. You want to use just the tip - no more than 1/4", and no more than 1/8" is even better - most beginners show far too much pick to the strings. For strumming chords, rotate your wrist a bit so the pick glides over the strings both ways instead of fighting its way through them on the way back up.

Hope that helps

When I first started, I got into the habit of only picking downward. Now I learned that you're supposed to alternate (Downward-Upward), and I have a lot of trouble picking upward.

jdb237,

Just play. Until you have 6 months [or 5 years IMHO] of playing under your belt you're still just getting started. Yes, everyone can point out counter examples to this but I'm talking general guidelines here.

Noteboat's advice about holding the pick is dead on so listen to him. At this point I hope that you're taking lessons from a good teacher or a group class. You need someone literally hovering over you, watching your technique as you build up good habits.

Also, I've taught hundreds of students, and they all suck at upstrokes when they're just beginning. It's kind of how it works. Just make sure that you're picking at the tip of the pick and keeping a firm grip. Bad upstrokes often come from not holding the pick tightly enough and letting the wrist get too wobbly.

Last thing: Practice alternate picking on ONE NOTE. Then learn how to apply it to a scale or exercise.