To keep it flexible and allow your users to still see old figures why don't you just move the months column as pivot prompt? (the prompt section of your pivot)
Or also add your month as a dashboard (or analysis) prompt.
If you don't want to allow your users to navigate to previous month the easiest solution would be to have a variable (repository) telling you what is the current period, and in your analysis you filter your month to the value of the variable.
Filter your report with Month(CURRENT_DATE)
Month(CURRENT_DATE) return a number, so that require the OP to have a column with the month number in his time dimension.
And the OP ask for the previous month, but I guess it's the previous month not based on the current date (we are in April and he refer to Jan-15 as the previous month).
Not knowing what other columns are available in his time dimension to produce the "Jan-15" value will be easier with the repository variable (and in that case the variable will always be correct based on the last data loaded in the DB).
In his pivot report i could see a date column, Also he has applied a year filter in the report. So hopefully with a date column in his report he can easily filter for month no.