Recently I did upgrade from 11202 to 11203.
Steps I followed
1. Grid should be up and running - Safe side I stopped the databases
2. Install + Upgrade - GRID to new GRID HOME
3. rootupgrade.sh will upgrade and start the grid processes.
4. Install - ORACLE to new ORACLE HOME ( just install software )
5. Upgrade database using DBUA from new ORACLE HOME.
Let me know if you have any more questions.