I write with my left hand is this makrooh or haram? should I start training with right hand?

Alhamdu Lillah

Writing with the left hand is neither prohibited, nor is it disliked, it is permissible.

The only thing must be done with the right hand is eating and drinking. Also, using the right hand for cleanliness after relieving one’s self is disliked, but not prohibited. Same for using the left hand for handling objects to others or taking it from others, it is also Makrouh. 

The Prophet SAAW said (Let none of you eat while using his left hand, as Satan eats with his left one and drinks with his let one).

As you see, the Hadith restricted the impermissibility of using the left hand to eating and drinking only. Other Ahadeeth indicate the undesirability of the right hand for cleanliness and the left hand for giving and taking.