Can you still get pregnant if ...

You have irregular bleeding. So I gave birth 4 months ago. Since then I’ve had 11 day periods and then I’ll start what seems like a period immediately after (really 3-4 days after) . But I’m wondering could I still get pregnant. I have sex rarely but often enough. I don’t use the pull out method or anything. But doctors refuse to give me birth control until this gets sorted out. But I’m kinda nervous don’t want to get pregnant while sorting this out. I could use condoms but is it even a chance I could. I googled bits of it and there was stuff like lack of ovulation and hormonal imbalances that could be causing this so if it was I wouldn’t be able to in that case ?? I’m going to the doctor on the 12 , they did an US to check for things to make sure I’m not already pregnant and stuff.