Yeah, that's your problem. I'm assuming you adding the priming sugar to the same vessel you were fermenting in and you didn't even stir. The sugar is going to be incredibly unevenly suspended in the beer so you're likely going to get many that are not even going to be carbed and a few that will terribly over-carbed.
Here's what you should ALWAYS do when bottle carbing: dissolve the priming sugar in boiling water and boil for 5 minutes. Cool and add to the bottling bucket first. Then, when you rack your beer from the fermentation vessel to the bottling bucket, the sugar water will naturally stir itself evenly into the beer. Bottle and cap as usual. Then give it at least 3 weeks at 70F to be fully carbed... "at least" being the key phrase.
I hope everything turns out alright