There are plenty of instances in which poskim relate their personal feelings in a psak. The first that came to my mind is R. Ovadia's famous ruling (Yabia Omer vol. 6, Even Ha-Ezer #3) that widows of soldiers missing during the 1973 Yom Kippur War not be considered agunot, a ruling that would allow those widows to remarry.
The psak is quite weighty, in which he takes pains to explain this unprecedented ruling of looking for leniency. The story behind this ruling has been covered by various historians, but here is how R. Ovadia's daughter, Adina Bar Shalom, described his experience:
He questioned the soldiers who served with the men missing in action. With each testimony, he cried. He couldn’t eat during those days, didn’t drink, didn’t sleep, could not close his eyes, until he gave a heter to every one of the wives whose husbands were missing. There were nearly 960 widows resulting from the Yom Kippur War. For many, the bodies of their husbands were found and identified. But [in those cases] where the bodies could either not be found or identified, as a result of my father’s pesak and thorough investigation of each and every case, not one woman was left an agunah.
The lengthy psak itself begins with R. Ovadia clarifying the weight behind this undertaking, in which he discloses his emotions:
ונפשי יודעת מאד גודל האחריות שבדבר, וכבד עלי הדבר מאד מקוצר המשיג ועומק המושג, אולם נתתי אל לבי מ"ש הרב הפוסק בשו"ת הב"ח החדשות (ס"ס סד) בפס"ד להיתר עגונה, להתיר בחינה קטנה שבבחינת העגונה הגדולה, שעליה אמר שלמה: ראיתי דמעת העשוקים ואין להם מנחם וכל מי שמתיר עגונה אחת בזה"ז כאילו בנה אחת מחרבות ירושלים העליונה להציל בחינה אחת מאשת חיל
My soul knows the enormity of this responsibility, and it is very heavy for me with insufficient knowledge of the concept. But I gave my heart in this...to permit in this great matter of agunot. As Solomon said: I saw the tears of the oppressed, and they have no comfort (Eccl. 4:1). Anyone who permits one agunah in this time, it is as if he rebuilt one of Jerusalem's ruins (Brakhot 6b), to save a woman of valor.