Google Sheets, use return value of a formula inside another formula

I have a google sheet with this formula:

=ARRAYFORMULA(may!B2:C)

It is accessing data from a sheet named may.I want to make it dynamic, so when next month comes it would change automatically to:

=ARRAYFORMULA(jun!B2:C)

I can get the actual month in a three letter format:

=LOWER(TEXT(TODAY(), "MMM"))

But how can I supply it to arrayformula? This does not work:

=ARRAYFORMULA(LOWER(TEXT(TODAY(), "MMM"))!B2:C)

Is it possible somehow?