Yes, it's poosible to get pregnant even though she has irregular periods, so I suggest you use condoms if you don't want parental responsibilities.
If she got her period the day after you had sex there is virtually no chance of being pregnant.
Pregnancy occurs when en egg is fertilised by a sperm.
When an egg is released itis called ovulation. Typically ovulation occurs approximately 14 days *before* the period begins.
The egg is only viable for around 36 hours after ovulation.
So to get her period the next day, ovulation is likely to have been around 14 days ago in which case the egg was long gone!