Selecting Month >= Month in Current Cell

I am trying to get a nested if function to flow where on Sheet 1 if in cell B4 based on the Selected Month in A1, if B3 is >= A1 go select from sheet 2 if not go select data from sheet 3. So if A1 has Feb and B3 has Jan, B4 should be selecting data from Sheet 3, because Jan is not >= Feb. See my test workbook for my attempt at figuring out the formula. Not to mention I don't think my index functions are pulling correctly.

Any help is much appreciated.