You're not being a sissy, its self preservation. I don't think you should give in by driving, because that sends the message that bikes don't belong. Rather, you need to speak to your local law enforcement and area elected representatives about the safety of this road.

Getting hit from behind is the most rare type of cycling accident. I'm not saying that it doesn't happen, but it happens only rarely. More what is likely is that drivers will not move over enough and give you enough room as they pass. I used to commute a narrow 2 lane section in NJ, also with no shoulders. WHat I found was the further right I was the closer the cars would pass, especially when there was oncoming traffic.

Move out into the road 2-3 feet. This accomplishes several things: (1) You have someplace to go besides dirt if someone tries something (2) As the car comes up behind you it will move further left and if you move slightly right as it passes, you will have more road. (3) Cars won't try to pass if there is no room- when there is oncoming traffic.

You could talk to your elected officials about adding a shoulder or bike lane or atleast a SHARE THE ROAD sign.