Along came a spider, and sat down beside her...

I've been wondering recently if fears are hereditary. Are they passed on or picked up? I've lived my entire life afraid of almost everything. Watching wind blow through the trees made me certain there would be a tornadoe. There was a time when I couldn't stay in school for even an entire afternoon without faking sick because of a "storm". My phobia was so intense that sometimes I would scream and cry uncontrollably. One of my worst memories is of my mother locking me outside the house one windy day because she thought I should "face my fears." I know she did it because she was at her wits end as to what to do with me and I don't blame her for it, but it was a terrible moment. I huddled by the door in what to me was "howling" wind and bawled my brown eyes out. The only storm that day was the one brewing between me and my mother.
Eventually I got over at least the intensity of that fear but there were others that took it's place. None so intense but nevertheless they are no less real. I am afraid of balloons, bugs, the dark, death, guns, getting our house broken into, being alone, and having bad things happen to my loved ones. I fear storms, serious illness, and failure. I always picture worst case scenarios. It's something I'm working on but it isn't easy.
I don't want my daughter to grow up afraid the way I was. I want her to be free from fear so she can truly fly. But sometimes I wonder if I have unconcsciously passed on my anxiety already.
For instance, she is already afraid of being alone. Except for in the morning or when she wakes up from her nap she will SCREAM if she is left alone in a room. She also is very afraid of falling. If I am not touching her while she walks she will cry. Even though she can almost do it alone or can do it pushing her walker. She needs to be holding both my hands or she will stand still and scream. I'm sure she'll get over this very soon but still I wonder if it isn't the first sign of other fears.
I am learning to be more brave, so if I am passing on my anxiety I hope she won't see to much. Yesterday when we went for a walk a spider crawled on her hat and I brushed it off without even squeaking! When she cries for me in the night I can walk across the house without turning on all the lights. And when thunder turns my house into a big base system I can be a big girl and pretend I'm unphased. I used to wonder how come my mom was never scared of anything...but maybe she just hid it well. Or maybe having kids is what helps us overcome some fears. (Although it brings on a whole bunch more!)
Do you struggle with fears? Do your children show signs of the same anxiety?