I just had this with my baby. I was told at 20 weeks it was low, I was re-scanned at 32 weeks and officially diagnosed with placenta previa with an anterior placenta. I was the told I'd be re-scanned again at 36 weeks. I have since found out that I should have been referred to see a consultant after my 32 week scan but never did and everybody I've spoken to since has been horrified at this so make sure your aware of what you should be entitled to.
The day before my 36 weeks scan I started bleeding so immediately phoned the hospital and went straight in. Once I got there I was bleeding really heavily and ended up having a c section that night. I lost more blood that usual because of my placenta - they had to cut through my placenta to get baby out - and felt awful for the next two days, I also ended up needing iron infusions but in the grand scheme of things that was nothing (I did feel like a pin cushion for the best part of the week). Baby is now 13 days old and still in special care as he struggled with his breathing and now isn't gaining any weight which is all because he was 36 weeks and a c section.
I'm sure you'll be ok but I'd just find out if you should be on any restrictions or taking any special precautions