It depends what you are logging in to.
You need to connect to the SQL server using windows authentication, that way your kerberos tokens are passed from the site, not the username/password. It is achieved easily in the web application's web.config:
<connectionStrings>
<add name="DBConnName" connectionString="Initial Catalog=Foo;Data Source=Bar;Integrated Security=SSPI;"/>
</connectionStrings>
Where the bold part tells IIS to pass the windows credential tokens across.
Then you need to grant the windows account running the IIS process access, details
here[
^].
Using your own account is a badish idea, if you change your password your site will stop working. You need to set up an account specially, note that in either case the account needs to reachable by both the IIS server and the SQL server so it must be in a domain both trust.
There is the usal dry advice from MS on the whole process
here[
^].