A private investigator who is a law enforcement officer can get phone records and text messages after applying for a warrant from the judge.
Then the warrant is handed to the phone company to get the text messages and other phone records.
However if the private investigator is hired privately and is not a law enforcement officer then no the private investigator cannot apply for any warrants so they cannot get text messages or any phone records.
A regular private investigator has no law enforcement powers and cannot get warrants, arrest you, get text messages, phone records or anything else.
The only things the private investigator can do is to follow you legally, take pictures, videos and then report back to the person who hired them on what they saw and where you've been.
They can then release the videos and pictures to the person who hired them.