Given you transferred your data directly from your old phone to your new phone, and that you no longer have your old phone, that leaves you with nothing as far as storage of those older text messages. It makes no difference if you use Smart Switch or some other service as a file transfer utility. since you apparently did not do any kind of backup step there's no place for you to bother looking into to find those older messages.
Just so this doesn't occur again, start using Smart Switch to make regular, full backups of your phone's user account data to a trusted computer if you have one, or into an online storage service. Backups are important,