I am new. I use shared godaddy.com hosting php account that doesn't support java.
I am interested in running my languagetool locally on my account, but not sure if that's possible given no java support.
The reason for running locally is to avoid per minute api limits.
Running your own LT server without Java isn't possible. You could upgrade to a better hosting offer that allows you to run whatever you want. These virtual servers are available starting at few Euros per month.