You ask for some way of completely eradicating irritability. The inclination to irritability is given us to use against sin, and we were never meant to use it against our fellow men. When we do, we act contrary to our true nature.
You describe how bitterly you regret the inefficacy of your prayers. Beware: to wish for consolation or revelation in prayer is a sure sign of pride. Pray humbly, in perfect simplicity, seeking salvation only through forgiveness, & having faith that God will extend to you His mercy - as He did to the publican.
In the eyes of God, it is always preeminently right that a man should spend himself in devising new means for spreading consolation to his subordinates, who are his charges.
The most important thing during illness is to offer to God patience and thanksgiving for His merciful visitations. Sickness purifies sins and gives one time to meditate on the past.
The abstinent withdraws from gluttony, the uncovetous from covetousness, the silent from wordiness, the pure from attachment to sensory pleasures, the chaste from fornication, he who is content with what he has from love of money, the meek from agitation (anger), the humble from vanity, the obedient from objection, he who is honest with himself from hypocrisy; equally, he who prays withdraws from despair, the willing pauper from acquisitiveness, he who professes his faith from denying it, the martyr from idolatry – so you see that each virtue, performed even unto death, is nothing but withdrawal from sin; and withdrawal from sin is a natural action, not an action which could be rewarded by the kingdom.
The enemy constantly endeavors to awaken in the abyss of the human heart a great turmoil about trifles. This is one of his tricks to blind our soul to the sun of truth, Christ our Lord, hidden in the heart's core of every one of our neighbors.
There is a sin which is always 'unto death' [1 Jn 5:16]; the sin which we have not repented. Even a saint's prayers will not be heard for the unrepented sin. The person who repents correctly does not imagine that his sins are cancelled through his own effort; but knows that through this effort he makes peace with God.