How can one get rid of the obsessive whisperings concerning the loss of provision and employment, and are there special supplications for that?

This feeling arises from having a poor opinion of Allah the Almighty. The cure for it is to improve your opinion of Him, and to have certain knowledge that what was destined to befall you could not have missed you, and what missed you could not have befallen you. Furthermore, Allah has apportioned provisions and lifespans, and you will not miss what has been decreed for you. Allah is also more merciful to you than your own mother, and nothing misses you except that He, Glorified be He, knows there is no benefit for you in it.

To attract, increase, and preserve sustenance, you must fear Allah the Almighty, for He says: "And whoever fears Allah – He will make for him a way out And will provide for him from where he does not expect." (At-Talaq: 2-3). Among the reasons for increasing sustenance is persistent seeking of forgiveness (istighfar). In the Hadith: "Whoever adheres to seeking forgiveness, Allah will make for him a way out of every difficulty, and relief from every worry, and will provide for him from where he does not expect." Among the reasons for increasing sustenance is persistent supplication (du'a). The Prophet, peace and blessings be upon him, used to ask Allah every morning after the Fajr prayer for beneficial knowledge, good provision, and accepted deeds.

So, trust in Allah and have a good opinion of Him. Do not worry about tomorrow, and know that Allah is the disposer of your affairs and your provider. Then, take the necessary means and strive to earn a living, while your heart remains attached to Allah the Almighty, knowing that all good is in His hands.