Multiple URL's redirecting the URI's.

Your iRule looks fine and should work, but you're repeating two very similar blocks of code. You could achieve the same functionality by using something like this with less lines

when HTTP_REQUEST {

     use getfield to capture the first field of the URI
    set uriField [string tolower [getfield [HTTP::uri] / 2]]
    if {($uriField eq "getstarted") || ($uriField eq "feedback")} {
        switch -glob [string tolower [HTTP::host]] {
               "*mywebsiteaz*" { HTTP::respond 301 "Location" "https://mywebsiteaz.com/web/xx/$uriField" }
               "*mywebsitefl*" { HTTP::respond 301 "Location" "https://mywebsitefl.com/web/xx/$uriField" }
               "*mywebsiteny*" { HTTP::respond 301 "Location" "https://mywebsiteny.com/web/xx/$uriField" }
               default { discard }
        }
    }
}

You could even do away with the switch statement if you used a datagroup for host to state lookups:

Datagroup:

ltm data-group internal states_dg {
    records {
        mywebsiteaz {
            data az
        }
        mywebsiteaz {
            data fl
        }
        mywebsiteny {
            data ny
        }
    }
    type string
}

irule:

when HTTP_REQUEST {
    set uriField [string tolower [getfield [HTTP::uri] / 2]]
    if {($uriField eq "getstarted") || ($uriField eq "feedback")} {
        set state [class match -value [HTTP::host] contains state_dg]
        if {$state ne ""} {
            HTTP::respond 301 "Location" "https://[HTTP::host]/web/$state/$uriField"
        }
    }
}