I Strongly urge you to get pre-approved before searching for homes for the following reasons.
You have the option to get pre-approved with any lender of your choice. Your best option will be Mortgage brokers than your banks. You tend to get better rates and lower fees with Brokers than banks.
I highly recommend Zero Plus Loan from Keller Mortgage. They not only have zero lender fees, they also give you $1000 towards closing costs if the loan amount is $150,000 or higher.
This loan is exclusively available for Keller Williams transactions only. Click here for Zero Plus Loan