I thought of a three-digit number. If I add all the possible two-digit numbers made by using only the digits of this number, then one third of this sum is equal to the number I thought of. What is the number I thought of?

You thought of the number 432.

I believe that the number is 198.

Using these digits, two at a time (but there is no restriction that the same digit isn't used twice), the possibilities are:

11,18, 19, 81, 88, 89, 91, 98, 99

The sum is 594.

Dividing this by 3, gives us i98.