We have a very common practice in our society for making Du'a for a special problem or what ever, by reciting a particular verse or Surah or a Du'a at a particular time for some period or number of days, is it a right Sunnah?

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

According to our knowledge, there is no specific Du'a (supplication) in connection with the state you have mentioned. But, whoever wants to solve his problems, has to fear Allah (to do what He likes and avoid what He dislikes), and then, his/her problems will be solved and sorrows relieved.
Allah Says (interpretation of meaning): {… And whosoever fears Allâh and keeps his duty to Him, He will make a way for him to get out (from every difficulty). And He will provide him from (sources) he never could imagine. …} [65:2-3].
In addition, Zikr of Allah (forms of remembering Him, reciting the Qur'an, Du'a, etc.) makes one's heart at ease and helps one to accept the Decree of Allah.
Allah Says (interpretation of meaning): {…Verily, in the remembrance of Allâh do hearts find rest.} [13:28].
Furthermore, praying to Allah is the best way to resolve problems and to drive away worries. But, Du'a is a form of 'Ibadah (worship); we are required to adhere only to what is confirmed in the Sunnah of Allah's Messenger (Sallallahu Alaihi wa Sallam).
In other words, you have to avoid some forms of Du'a or Zikr that are not confirmed in the Sunnah.
Allah knows best.