I have just immigrated to the US, where do I take my child to get checked up about a vaginal infection?

You can utilize clinics like Planned Parenthood or public health systems. These clinics provide some free or low cost services, like if there is concern for an infection, birth control services, or even general health check ups. Check to see what is available in your community. Many of these places also take care of undocumented people without fear of deportation or reporting immigration status to ICE.