Another example of why using a lawyer to prepare TN petitions is a waste.
You neglected to ask that in your original post. hd you, you would have been told not to bother going to border. 3 months was WAY too soon.
Just so you know in future, the border doesn't do "extensions", so do not ask for an extension if you ever apply at border again. They issue "fresh" TNs, with expiry dates no more than 3 years from the day you present the petition, based on the current-dated TN letter you present (it doesn't need a start date -- it needs a stated time period of employment of no more than 3 years). And when the TN has the same sponsor/job/category they typically only give new TNs just as the old TN is about to expire (2-4 weeks).
If you wish to now file by mail (using form I-129), that is up to you, but I wouldn't bother with premium processing. Your current TN is valid for 3 months PLUS the 240-day grace period while I-129 processing takes place.
The company has already wasted money on a lawyer who was not competent in TNs. Are they going to pay him to prepare your I-129?