Oh mama! I wish I had things to say to you that I wasn't afraid would sound scary. I'm sorry I don't, but this is a scary condition, and talking about it just isn't soothing. I had placenta previa with my DD, who is a year and a half old now. She was born at 32w4d, by c/s, due to hemorrhage. I would definitely have preferred to give birth vaginally, at home or in the most homelike birth center imaginable (and at least six weeks later than I actually did), but my c-section was a very positive experience nonetheless. My daughter and I were very well cared for, and the hospital did everything they could to facilitate contact between us, even while treating DD for the complications of prematurity.
I am so sorry that you are in this situation. There is nothing about placenta previa that does not suck. However, I'm also going to congratulate you. You made it to 37 weeks! Many, many previa cases result in pre-term delivery, and you are past the risk of that - if you were here, I would throw you a party. But it's also a stressful time, because labor with this condition is so dangerous. I hope it's gone away and all this winds up not being an issue. While you're waiting to find out, please be careful. Try and make sure there is someone in your house who can help you, and keep a phone close to hand.
If any part of the placenta continues to cover the cervix, I am sorry mama, but you really do need a c-section. You absolutely cannot birth vaginally with this condition - the risk of you and the baby bleeding to death is incredibly high. Usually, when people say things like this, they are being alarmist and ridiculous. With placenta previa, it's actually true. If you experience bleeding or start to go into labor, you need to get to the hospital immediately.
Would it make sense for you to schedule an appointment (like, Monday) with your OB to discuss what will happen if the placenta isn't clear of the cervix? Can you sit down and talk about what you want for you and the baby? Some hospitals are very accommodating of immediate contact, bringing you the baby and holding her in contact with you while the surgery is finished, and keeping moms and babies together in recovery. Some hospitals that aren't usually very accommodating can be convinced to be flexible if you make your wishes known. Advance notice helps, but don't be afraid to speak up even if you wind up going in as an emergency.