No. If that were the case, you and I would be bombarded with notifications all day long – and there is no need for someone to know your public or private IP address. What would they do with this information? It is used for automatic routing of data packets, not for human use.
Your IP address changes if you move your computer to a different network (such as from home to office). It will also change randomly during the day or week, depending on how your router is configured. As to your public IP address, that may also change daily depending on how your internet provider has configured their routers.