Praise be to Allah.
Allaah has permitted us all the produce of the sea: Lawful to you is (the pursuit of) water-game and its use for food [al-Maaidah 2:96 interpretation of the meaning]. The Prophet (peace and blessings of Allaah be upon him) told us that it is halaal (lawful) to eat dead creatures from the sea and dead fish, and no part of the fish was excluded from this permission. Hence we know that all parts of the fish are halaal, including its skin, tail, eyes, etc.
It is strange indeed that a person could dare to forbid something that Allaah has permitted. This is a very serious matter, as Allaah says (interpretation of the meaning):
O you who believe! Make not unlawful the tayyibaat (all that is good) which Allaah has made lawful to you, and transgress not. Verily, Allaah does not like the transgressors. [al-Maaidah 5:87]
Say: Who has forbidden the adornment with clothes given by Allaah, which He has produced for His slaves, and al-Tayyibaat [all kinds of halaal (lawful) things] of food? Say: They are, in the life of this world, for those who believe, (and) exclusively for them (believers) on the Day of Resurrection (the disbelievers will not share them). Thus We explain the aayaat (Islamic law) in detail for people who have knowledge. [al-Araaf 7:32]
Say: Tell me, what provision Allaah has sent down to you! And you have made of it lawful and unlawful. Say: has Allaah permitted you (to do so), or do you invent a lie against Allaah? [Yoonus 10:59]
Allaah has also warned His slave against forbidding anything without knowledge. He said (interpretation of the meaning):
And say not concerning that which your tongues put forth falsely: This is lawful and this is forbidden, so as to invent lies against Allaah. Verily, those who invent lies against Allaah will never prosper. [al-Nahl 16:116]
This person who has invented a lie against Allaah by saying that it is haraam to eat the eye of a fish must repent to Allaah, and not go beyond the limits in talking about the Religion of Allaah. He should not speak without knowledge. Even if he is put off by something or feels disgusted by it, he has no right to say that it is haraam. The Prophet (peace and blessings of Allaah be upon him) hated the smell of garlic, and said: Whoever eats anything from this unpleasant plant should not approach us in the mosque. The people said, It has become haraam (forbidden), it has become haraam. When the Prophet (peace and blessings of Allaah be upon him) heard what was being said, he said: O people, it is not for me to forbid something that Allaah has permitted; this is just a vegetable whose smell is unpleasant.(Reported by Ahmad and Muslim, 877). The Prophet (peace and blessings of Allaah be upon him) explained that the fact that he disliked garlic and told people not to come to the mosque after eating it did not mean that it was haraam.
Although the Messenger of Allaah (peace and blessings of Allaah be upon him) disliked the idea of eating lizard-meat, he did not forbid others to eat it, as is reported in the following story:
Khaalid ibn al-Waleed reported that some grilled lizard meat was brought to the Prophet (peace and blessings of Allaah be upon him) and put in front of him. He stretched out his hand to take some, but one of the people present said, O Messenger of Allaah, it is lizard meat, so he pulled his hand back. Khaalid ibn al-Waleed asked, O Messenger of Allaah, is lizard haraam? He said, No, but it is not known among my people and I cannot face eating it. So Khaalid took some of the lizard meat and ate it, whilst the Messenger of Allaah (peace and blessings of Allaah be upon him) looked on.(Reported by al-Bukhaari, 4981, al-Nisaa'i, 4242, and Abu Dawood, 3300).
After explaining this answer to you, I want to warn you about something that I noticed in your question, where you said that you went to the seafood restaurant with a male friend. If this person is not your husband or a mahram (blood-relative whom you are permanently forbidden to marry), then you should fear Allaah. Ask yourself: which is more serious, eating the eye of a fish or going out with a man to whom you are not related to sit and chat with him in a restaurant?
I ask Allaah to protect us from all things that earn His wrath and to help us remember and fear Him. May Allaah bless our Prophet Muhammad.