Dear Mr. Mahmood, Wa-alaikumus salam
There are several remedies such as: cuasticum, veratrum, hyoscyamus, stramonium, merc sol, phosphorus, silicea, tuberculinum, argentum nit, bufo, belladonna, coccculus, etc., that can help a patient with stammering. Though you have given a good deal of information about your problem, yet a lot remains to be ascertained and that can only be done in a clinical setting.
Homoeopathy will help you, In shaa Allah but for that you will have to see a good homoeopath in your city. He will take your case and prescribe a medicine most suited to your problem.
Wishing you all the best,
Ahmad Fakir Muhammad, Homoeopath