Will a country that cares for its environment be affected by climate change due to other countries' pollution?
The main driver for anthropogenic climate change is carbon dioxide because it is very long-lived and hence relatively evenly distributed within the atmosphere. And even if you'd somehow manage to keep reduced levels of $CO_2$ in your country's atmosphere, you'd still be affected by large-scale weather changes. So yes, your country would be affected just like any other country.

Of course other benefits from climate-friendly policies, such as better air quality due to reduced combustion or better public transport due to investments in that sector, have a stronger local impact.