Yes! It is true that your mass and, in fact, every single mass in the universe affects every single other mass in the universe gravitationally. This can be seen through Newton's equation for gravitational force: $$\vec{F}_\mathrm g=G\frac{m_1 m_2}{r^2}$$ where $G$ is the gravitational constant: $$G\approx6.67\times10^{-11}\ \mathrm{\frac{m^3}{kg\ s^2}}$$
$m_1$ is the mass of one object (let's say your mass), $m_2$ is the mass of the other object and $r$ is the vector denoting the distance between your two objects. As you might notice from this equation, the only way to have $F_\mathrm g=0$ is if one or both of your masses are equal to $0$. As long as the two objects you are measuring the force between have some measurable mass, they will experience a gravitational force, no matter how small.