I use a random number generator to generate normally distributed numbers. The problem is negative numbers are unphysical in that particular simulation. So I use "if/else" to discard them.
My question is: What is the resulting distribution? It's obviously not Gaussian any more since it is cut on the left.
I think if you search for truncated normal distribution you will find what you want.
In your particular case, the density function is given by
$$f(x)=\frac{1}{\sigma}\frac{{\phi\left(\frac{x-\mu}{\sigma}\right)}}{1-\Phi\left(-\frac{\mu}{\sigma}\right)}$$
where $\phi$ is the standard normal density:
$$\phi(z)=\frac{1}{\sqrt{2\pi}}\exp\left(-\frac{1}{2}z^2\right)$$
and where $\Phi$ is the standard normal distribution.