iRule with Uppercase Letters in the URL

Try this:

when HTTP_REQUEST {    
    if { ( [string tolower [HTTP::host]] equals "x.x.com" ) and ( [string tolower [HTTP::uri]] starts_with "/mytest" ) } {        
        if { not ( [HTTP::uri] starts_with "/MyTest" ) } {            
            HTTP::uri [string map -nocase {"/mytest" "/MyTest"} [HTTP::uri]]
        }
    } else {        
        HTTP::redirect "http://x.x.com/MyTest[HTTP::uri]"
    }
}    

Better to not do the pooling in the iRule if you can help it, as the status of the monitor status of the assigned pool directly affects the status of the VIP.