Is it possible to change my public IP address from dynamic to static?
No, not unless you have a business broadband account.
Your question was answered here last time you asked
I have friends trying to connect to me over an online game and it constantly changes.
As mentioned, you can't have a static IP address on residential service.
The IP address you have shouldn't constantly change, but certainly may do when rebooting your router, turning off the router or a reset has occured for some reason. However as it's a dynamic system, you can't specifically host anything unless you use a service as given to you in another thread as Keith has said.
If your friends access your computer using your host name, instead of your IP address, then they will automatically be directed to you current public IP address.
Your can test this by pinging your new host name, and seeing if it returns the same value as if you visited this website
So if your host name was chrisbrem.noip.org
Then pinging chrisbrem.noip.org
should give you the same IP address as http://www.whatismyip.com/
If it does not, then you have a setting wrong on your home hubs dynamic IP page.