Please don't open RDP to the internet and rely on using a different port to `provide security'. Merely picking different ports does almost nothing, your machine will be scanned and the altered RDP port discovered almost immediately. RDP across a LAN or VPN are potential options though. Another TeamViewer like program is
ConnectWise Control (formerly called ScreenConnect) Free. I used the payware version at a previous employer and preferred it to TeamViewer.