I want to know the solution for social phobias and public speaking problems according to Qur'an and Hadith. Please reply.

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

The cure for doubts, fear and nervousness is to rely on Allah, and have trust in Him, and be absolutely sure that everything is in the Hands of Allah.  Whatever Allah wills to happen will happen, and whatever Allah does not will to happen, will not happen.

Allah, the Most-High, is the One who has the right to be remembered, and worshipped.  He is the One Who gives help and support to those who seek help and support from Him, He is the Most Merciful of possessors, and the Most Generous of those who were asked, and He is the Most-Generous of those who give.  He is All-Aware of everything, and He, the Most-High, Knows what is in the land and what is in the sea, and there is no leaf that falls but he Knows it.  There is not a grain in the darkness of the earth nor anything fresh or dry, but is written in a Clear Record.  So how can one who is blessed with the sweetness of Iman fear predestination, while he knows that what befalls him is not to miss him and the victory comes with patience, and verily, with hardship there is relief and if all the creatures of heaven and earth unite to benefit him they can not do so and if they decide to harm him they can not except of what Allah had written in Divine Decree. How can one who Praises Allah fear while he knows that thunder glorifies and praises Allah. The Heavens and the Earth Praise Allah as well.  The birds also have their Salat and their glorification (glorifying and praising Him in their own way and manner).  How can one fear when he knows that Allah is full of kindness and Most-Merciful, and he is more Merciful to you then you are towards yourself?  How can one fear whom he knows that Allah is the Irresistible (Supreme) over His slaves?  Everything that exists in the universe belongs to Him.

The slaves that rely on their Lord do not fear anything.  The creatures as well do not fear as Allah is their Supporter and Sustainer.

Therefore, if one considers all that is mentioned, or even considers just some of it, he will indeed be blessed by Allah with peace and tranquility.  But the most important of everything, is the remembrance of Allah, as Allah Says (interpretation of meaning): {…Verily, in the remembrance of Allâh do hearts find rest.}[13:28].

Allah knows best.