Confusion over a static IP address using self hosted OpenVPN

I would have asked this elsewhere but the OpenVPN forums won't allow new user accounts at the moment so hoping someone here can assist or clarify things.

I need to access an IPMI server from a static IP address but my home connection is dynamic.  I thought I could simply use a VPN to fix this but am a cheapskate so wanted to try to do it with something free.  I set up a free tier AWS instance and installed OpenVPN, got it running and can connect to it using the desktop app at home. 

I was assuming that doing so would change my public IP as it does when I use something like Private Internet Access or Nord.  I was also assuming that this would change my home IP to be the IP of the server I have OpenVPN running on.  However when I ask Google to tell me my IP address it still shows the home (dynamic) IP even though OpenVPN claims I am connected.  In the OpenVPN app it says my private IP and server public IP are two totally different numbers than what Google is reporting to me.

Am I misunderstanding what OpenVPN can do for me in this regard?  All I need is a way to get a static IP address (no, my ISP doesn't provide them).