Blood thinners

I am 17w pregnant and my new OBGYN is putting me on a blood thinner as my leg threw 2 clots in my last pregnancy and one postpartum. Lovenox injections is what I believe my med will be. Anyone have any experience with this type? I was on xarelto before my pregnancy and that stuff made me dizzy I assume because of the thinner blood. Any noticable sideffects? I know my risk for hemorrhage will be higher on a blood thinner but what can I do? It’s damned if I do and damned if I don’t. So I’d rather protect my plecenta/lungs/brain/heart.