Trinicalm Plus contains trifluoperazine + trihexyphenidyl (also called benzhexol) while Trinicalm Forte contains chlorpromazine in addition to the other two medicines. In other words Trinicalm Forte is three-in-one combination product. In good clinical practice one should try to use the various drugs separately, if at all required, rather than in one tablet because side effects can get multiplied. In advanced countries such irrational combination products are not permitted. Even in India, they are being marketed without legal sanction from the Drugs Controller General, India (DCGI).
All the three medicines are not to be used in patients with liver impairment. There are so many other drugs that can be used. Since you have not given the exact diagnosis, I am unable to offer concrete advice. Mental problem is a vague term.
I do not know why your doctor has prescribed this medicine. With regard to the use of Livfit - an Ayurvedic preparation - we are unable to comment on its safety and efficacy. Allopathic doctors are legally prohibited from using Ayurvedic preparations as per Supreme Court Orders (Reference: Poonam Verma v/s Ashwin Patel & Others Appeal number 8856 of 1994).