If i have social anxiety, does that my daughter will as well?

No: Although such things seem to run in families, any problem like that is a product of both genetics and environment. Create the most supportive environment you can, help her learn and master as many skills as possible, and help her engage in and feel comfortable in as many social situations as you can, and you will minimize the chance that such anxiety will develop.

At higher risk: A child with social anxiety (phobia) often has a family history of excessive shyness or social anxiety.