I would like to know if there is a Mitzvah to be Machmir. For example, if there is a kosher Eruv in my town do I get a Mitzvah for not using it? Another example, does one get a Mitzvah for keeping Chalav Yisrael?

It is difficult to justify the term “get a Mitzvah” though in many cases I would agree that a Chumrah may be a higher fulfillment of a particular Mitzvah. However, we should be careful, as a Chumra is an attempt to serve HaShaem more perfectly, and not relying on an Eruv, in cases, may cause jealousy, hardship, or discomfort that may be contrary to the ideas of the service of HaShem. One should discuss specific Chumrot with a Posek before deciding that they will enhance one’s service of HaShem.