The conservative perspective (which sounds like an oxymoron, since I said conservatice) of Date of Viability is 24 weeks or six months. The earliest baby was born at 5 months, 1 week (or 21 weeks, 5 days) but that doesn't mean that's the latest point in which you can have an abortion. You can have one up to 23 weeks, otherwise you will have to wait it out. Have the OB/GYN ask routine questions, don't try to figure out conception yourself. They've studied for this stuff, and with the proper testing and scanning, they can tell you how far along you are... and whether or not you can have an abortion.
Like Lizzie said, we're concerned about you now because we don't want you to hurt yourself. Getting pregnant isn't the end of your life or the world, no matter how conservative or strict your parents are. Plus, you were raped, and you can only do so much to prevent that from happening. If they can't accept you were raped, don't want this baby, and you are planning on killing yourself, then they're not meant to be in your life. Find people who are more supportive of you, more caring, more willing to stand by your side and stop you from hurting yourself.
As Lizzie said, the family adopting your child will be the ones to pay for the medical expenses. You don't have to worry about paying for anything.