Here is one using only DAY(), MONTH() AND YEAR() functions:
SELECT * FROM MyTest WHERE
year(@today)=year(@lastday) and month(@today)<month(@lastday) and
( month(birthday)>month(@today) and month(birthday)<month(@lastday)
or month(birthday)=month(@today) and day(birthday)>=day(@today)
or month(birthday)=month(@lastday)...