Dry hopping is not the culprit here. Neither is 2-3 weeks for bottle carb/condition. (3 weeks is minimum for this process and it usually only improves the longer you give it). I would suggest a few things.
1. Did you use the priming sugar included in your kit? This is usually 5 oz which yields normal to high carb level in most beer styles.
2. Did you put your bottles in fridge before drinking? Cooling them helps dissolve the co2 into the beer better and reduced the chance of overflow.
3. I would HIGHLY suggest pouring your homebrew into a glass before drinking. As you place your bottle down, you'll release co2 from in solution and it may force the beer out the top of the bottle. Even more so, your home brew has more sediment/yeast in the bottom of your bottle that will get mixed back into the beer if you are constantly moving or shaking the bottle, as happens with drinking. Pouring it will allow you to leave this sediment in bottle leaving clearer, cleaner tasting, and less gas producing beer.
I think your gusher problem is a combination of the above points. Try refrigerating for a few days prior to drinking, pouring into a glass leaving the last 1/4 inch of beer, and next time, use an online priming sugar calculator to determine the amount of sugar needed to carb your batch.