Caffeine content in tea?

The caffeine content of your tea is, for many reasons, impossible to calculate from the information you have provided. You didn't specify what type of tea was in your bag, where it is from, when it was harvested, how it was harvested, your steep times...

However, some things are definite.

Your tea, all three cups together, has less caffeine than an 8-oz house coffee.

If you kept the steep time constant, the first cup would have the most caffeine. However, since you increase the steep time and the first steep is so short, I would guess they are all about the same.

Edit: If you read the link I posted, you'll understand why you need such specific information. Tea from the same area of just one plantation can vary fourfold in caffeine over the course of a year - imagine then mixing it with teas from other plantations at random times of year. All you're going to get is vague qualitative answers rather than specific numbers without your own mass spectrometer.

I don't know the exact mathematics behind extraction, unfortunately, but my impression is that the first two steeps are about equal in strength and the third is likely to be the highest in caffeine.

Coffee has on average 2-3x the caffeine of tea. So if you drink enough tea it could keep you up. So many things have caffeine, that something else may be adding to your problem. In fact, a 5oz bar of extra dark chocolate has as much caffeine as 1 cup of coffee, so if you're eating chocolate that could do it too. See the link below for the caffeine content of many things you may be consuming.