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If the condom slipped off and your partner did not ejaculate in you then there is no chance that you could be pregnant. However if he ejaculated at the mouth of vagina then also the sperm can travel up and cause pregnancy.
Even if your periods are irregular you can calculate the longest time after which you had periods and take a pregnancy test after that.
If you have irregular periods and are new to sexual activity, then the best thing is to consult a gynecologist and get an examination done and go on pills. There are many pills which offer contraceptive protection right from the first month. Hope this helps. Take care!
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