Can your baby be transverse and the head be engaged at the same time?

With my first pregnancy I was told over and over that my OB could feel the baby's head and that it was engaged. So when I went into actual labor I was told the baby was transverse so she had to move the baby or something. I was just a bit out of it so I don't remember much else but that, but I remember being confused because how could the baby be head down and transverse? So I'm 39 weeks pregnant with my second and I know with your second the head doesn't really engage until labor since it just floats, but I figured it was head down since I do feel sharp twinges of pressure in the l area rather often. The big thing that throws me off is that I have a slight heart shaped uterus and my baby gets the hiccups a lot. I feel the hiccups on my right side right above my right thigh and then I feel kicking or punching way over on the left middle of my belly. To me it sounds like my baby is transverse again, but I'm wondering if it doesn't even matter since my first came out just fine after everything. Any thoughts??