You say you made this change "the other day". How long ago was "the other day"? Have you already received a bill? How much was your bill last month? How much is it this month? Have you looked at your "detailed bill"? ALL charges are itemized in your detailed bill. I suggest looking at your "detailed" bill instead of your "billing summary" to determine why your bill went up $10 if you chose a data allowance which was $10 cheaper.
It would also depend on HOW you made the switch. If you made the switch effective immediately, you could be charged overages. If you made the change effective at the beginning of your "current" billing cycle, you SHOULD see a lower bill after the change by $20 and then increase by $10 the following month to be only $10 lower than you old plan.
You may ask HOW can I have overages if I am switching from a 3 GB plan to a 3 GB plan. This is all due to pro-ration. Say you made the switch effective immediately at the halfway point of your billing cycle but had used 2 GB of your data already. Your data allotment for the old plan would have been 1.5 GB at the halfway mark, yet you used 0.5 GB over that amount meaning you would have a $15 data overage during the 1st half of the month on your old plan. You would get another 1.5 GB to use on the new plan for the 2nd half of the month. You have to be VERY careful when changing plans mid month to take effect immediately. Unless you fully understand pro-ration, you should make a switch effective either at the beginning or the end of your billing cycle.