Hiding your IP should be your minor concern. First an IP address for a client device like a smartphone is generally not a fix IP. But if you use the application that is installed on your smartphone, your ISP should know at what time exactly you have sent the message. If you only want to be hidden from your little cousin, that should be enough, but if for any reason a legal action was started, your ISP could have to give to the authorities the list of the phones that sent Instagram DM in the requested minute. Then never forget that the police can use data from several sources to reduce their investigation field.
What I mean is not that you will be immediately tracked. I just mean that if the police of your country has serious reasons to find the author of a message, they will use many other elements than the IP address. In fact IP is mostly something that is easy to use in police series, but in real world I would never try to use an IP address to find somebody, because it is really too easy to mask it. Language, wording, times, version of the application and the OS are far better markers! They cannot be used alone if you have no suspect, but if you have a reduced number of suspects it will be easy to find which one is guilty.
