Hi Jinnyann,
Maybe the 'alternative' therapies idea is to berid you <font color="blue"> </font> of the effects (blockages, stoppages etc.) to your natural thoughts and feelings. To get to the authentic 'you'.
It may not be the best case scenario for you - it may be too much of a sudden mental 'confrontation' for you, with which you could feel more overwhelmed with any issues that you are currently on the medication for.
It maybe, though, just what works for you.
If you are feeling really uncomfortable with the possibility of placing yourself in a (perceived) more vulnerable emotional position by going 'cold-turkey' with the medication, as suggested by the 'natural' therapy clinic, consult with the physician, who prescribed them in the first place, and 'run-by' him your desires to try this method. He/she may work with you to explore a medication-reduction combined with gradually 'opening-up' (talking and experiencing) the natural, (gradually unaffected by medication), 'you'.
Ultimately, it is a decision, with excellent support, that you need to make for yourself. But do it as safely as possible. You want the best for yourself and the safest outcome.
I wish you well.