Its one account per person, not per ip or per computer.
So getting a new computer won't cause any issues, logging in else where won't either. I log in from work time to time and from my phone as well.
Now if you have someone else you share wifi with that gets locked and/or scammer tagged, its possible it may affect you as well. So be mindful of that.
I generally avoid public wifis as a precaution against that.