Go into Chrome and click on the three-dot menu in the top right-hand corner. Then choose Settings.
At the top you will see your Account you signed in with to Chrome. It will most likely say "Syncing to....". Click on the account and it will show you a page showing you the account(s) you have signed into Google on your phone. Click on Sync below the account list and then disable Sync to disable any sync with your home Chrome. Or you could tweak it in the section below by turning off Sync Everything and then only enabling the things you do want to sync (i.e. Passwords).