I have a hosting plan through Godaddy that only supports python 2.6.6. I have been able to install python 2.7 and 3.6 through SSH and run scripts, pip, no problems.
When I try and run a PHP script that calls a python script from SSH, it works just fine using my new python installs, but when I open the PHP script in a browser, it will only run 2.6.6.
Why is this? Is there a way to get around this without getting a VPS?
I think what is happening here is that you are able to manually run Python3 from your SSH session by calling it directly.
However, your PHP installation probably isn't aware that you have more than one instance of Python installed. At a guess, your PHP installation is defaulting to it's environment path (or other predetermined library directory) where it can find a Python installation (this installation being the original 2.7).
I'm not sure how you are calling your Python scripts but there is an answer here: Calling specific version of python from PHP that talks about changing the python version in the script.
Another possible solution is to add the directory containing Python3 to your $PATH variable. Word of warning, if this is a shared system this might be disabled or potentially COULD get you in some trouble. Since altering the path might start other python scripts (belonging to other people) being called by Python3, which could break them (due to deprecated syntax etc)
When you want to start messing with system configuration, you're getting into VPS territory rather than shared hosting.
I have found a sneaky way around this. I used SSH2 PHP extension to call the python3.