Does the Ringing of the Ear Mean bad omen in Islam?

There is no basis for regarding ringing in the ears as good or bad omen in Islam. The Muslim has to put his trust in Allah. Regarding things as bad omens is a kind of belief in evil omens, which the Prophet (peace and blessings of Allah be upon him) declared to be false and stated that it is a form of polytheism. 

If a person notices any such thing (ringing in the ears, etc.), he should ignore it and go ahead with his plans, and not hesitate. 

The Prophet (peace and blessings of Allah be upon him) said: “Tiyarah (superstition) is that which makes you go ahead or refrain.”

The Muslim should also recite the following Du`a: “Allahumma la yu`ti bi’l-hasanat illa anta wa la yadfa` as-sayi’at illa anta, wa la hawla wa la quwwata illa bika (O Allah, none can bring good things except You, and none can ward off evil things except You, and there is no power and no strength except with You).”

As for seeing something and interpreting it in an optimistic manner, this is good, and the Prophet (peace and blessings of Allah be upon him) used to like optimism. Optimism means thinking well of Allah. 

For more details, please refer to the following answers: 46985 , 97221 , 2039 , 33842 , 126359 , 33844 , 362868 , and 8291 .

And Allah knows best.