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If you have stopped taking your birth control and have been sexually active without additional protection, chances of pregnancy are possible. The spotting/bleeding after intercourse is not normal and should not be ignored. If you suspect pregnancy chances, visit your doctor/gynecologist at the earliest for thorough examination (to confirm pregnancy related changes/signs in body) and blood/serum HCG level test (to confirm/rule out pregnancy accurately). If pregnancy gets confirmed, you should go ahead with further evaluation to rule out chances of low lying placenta, bleeding from placental separation, retroplacental bleed, etc. Getting serial HCG levels estimated also helps. Doubling up of the hormone levels in 48-72 hours will show that pregnancy is going on smoothly. If levels are not adequate, then external hormonal supplements would be considered to be started to help you in preventing miscarriage/threatened abortion. An early ultrasound scan done will also help to know if pregnancy is viable and look for the source of bleeding. Be in regular monitoring and follow-up with your treating doctor/gynecologist and report any new/abnormal symptoms immediately.
Take care.