My period came on the 38th day last month... does it mean it will come on the 38th day this month too?

Past history: Let past history be your guide. If you typically have a 38 day cycle each month then it is likely that will continue. If you typically have them more frequently but only last month was “off” then it is more likely you return to normal in the future. If you are always irregular then you will likely continue to be irregular. It is hard to predict knowing only 1 months history

Maybe. Maybe not.: Since our calendar months have no more than 31 days, the "38th" day must mean a 38-day-long menstrual cycle. The length of one cycle predicts the length of the next cycle ONLY if cycles are regular, but not if cycles are irregular. Thus, one would need more information before guessing how long this current cycle might be.