Could i be pregnant even though i've been having breakthrough bleeding all month from starting birth control for the first time?

Not likely: No birth control method is 100% even with perfect use (no missed or late pills), the failure rate is 0.3% (less than 1 couple/100 will get pregnant in the first year of use) or 9%-9/100 will get pregnant with typical use..You should do a pregnancy test if you're worried or have missed pills, but bleeding in the first or second month after starting pills is common (even with perfect use).