Did you install Grid Infrastructure as oracle user or grid user?
Did you update the environment variables ORACLE_BASE, ORACLE_HOME, PATH etc..
To upgrade ASM after installing Grid, you must use ASM Configuration Assistant ASMCA.
Pls provide the exact steps.
You dont need to upgrade ASM because its already the part of GridInfrastructure. Just mount your disk groups from 11g ASM instance.
You can paste the error message you have got for corrupted grid installation.
As told previous you need not have to drop and recreate the ASM instance on 11g.