I assume that your months are entered as text, in the manner appearing
in your message. Then, the following *array* formula (needs to be
committed with Shift+Ctrl+Enter) should do:

=AVERAGE(IF(AND(DATEVALUE("1 "&A1:A100)=DATE(1990,1,1),DATEVALUE("1
"&A1:A100)<=DATE(1990,3,1)),B1:B100))

HTH
Kostis Vezerides