i can try increasing the weight, but then my reps would be much less than 15-20. would that matter? And i find that with heavier weights, i'm more inclined to use momentum and swing the weight which is not what i want to do.
Doing 15-20 reps isn't really challenging to the muscle, you're really just training the muscles for stamina when you work in that rep range. Try going down to ten reps with a weight you can handle at that range, you'll most likely see more results. When it comes to swinging the weights up, there's an easy remedy there- Don't do it.

If you can do an exercise with good form at fifteen to twenty reps, then you should be able to drop the reps down, and find a weight you can still use with good form at your new rep range- Definitely do not swing the weights, stick with proper form. It might take you a while to find the right amount of weight to use for each exercise, but you'll get there-
most of all to the point of burn and exhaustion, which is what i read in the magazines.
Burn and exhaustion have nothing to do with progress really- You can reach all your goals without them, so don't rely on them to know whether or not you've had a good workout- Rely only on your results. Yes, it can take time to see results, I'd recommend waiting three or four months when you start a new program to see if it's really working for you- The body takes time to adapt.