All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad, ﷺ, is His slave and Messenger.
We ask Allah, the Exalted, to grant your father complete healing, to bless him with well-being, to raise his ranks, and to expiate his sins and misdeeds.
As for a woman traveling without a mahram, the majority of scholars hold that it is not permissible without necessity, because of the ahadith that forbid it, such as the agreed-upon hadith: “A woman should not travel except with a mahram.” [Bukhari and Muslim]
Some scholars hold that it is permissible for her to travel if a mahram cannot be found and fitnah (harm) is not feared.
Accordingly, the more cautious course is not to travel without a mahram if there is no genuine need for you to be with your father.
However, we see no objection to your following the opinion of those who hold that a woman may travel by airplane, and they consider it equivalent to safe company (al-rufqah al-aminah)
We also draw attention to the obligation of a married woman to seek her husband's permission, so she should not travel except with his permission.
Allah Knows best.