The US Geological Survey is best known as the source of maps of topography and geology in the United States. But the USGS is also a source of water information, particularly stream flows and ground water information. In addition to the gauges that monitor rivers across the country, many of the gauges also have a rain gauge. The data can be accessed and is particularly useful in areas where there are no other rainfall measurements.
This link https://ga.water.usgs.gov/precip/ provides access to real-time precipitation data across Georgia, and you can get to other states by substituting that state’s abbreviation for “ga” in the link. Other parts of the USGS site provide graphs of past streamflow and precipitation such as the one shown below.