On carefully inspecting this question, one can understand that there are two days which are important and these are:
A. My Birthday.
B. The day when I am making this statement.
If you think for a while, you will understand that such statements can be made only around the year’s end. So, if my birthday is on 31 December, then I will be making this statement on 1 January.
I will further explain using the following example:
1. Consider that today is 01 January 2017.
2. Then, the day before yesterday was 30 December 2016 and according to the question I was 25 then.
3. Yesterday was 31 December 2016, which happens to be my birthday too (Woohoo!), and my age increases by one to become 26.
4. I will turn 27 on my birthday this year (31 December 2017).
5. I will turn 28 on my birthday next year (31 December 2018).
Now, if you read the question again, it will make more sense:
The day before yesterday(30 December 2016), I was 25 years old and next year(31 December 2018) I will be 28.