The former Bohemians frontman was chosen as Town's central striker for the season-opening 2-1 defeat at Port Vale last Saturday.
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Head coach Brown said of the injury: “It's not a nice one but he's looking a lot better and he can open his eye. He has meetings with consultants.”
“He was very brave going in for that challenge, which was just two players wanting to win the ball … but their player was a bit quicker.
“Promise hadn’t started badly. He put a shift in and has an assist but he has a lot to learn.”
Brown admits that fielding Omochere ahead of the more experienced Joe Garner and Ellis Harrison, who both came off the bench, may have been a mistake.
He added: “We played Promise for his pace and maybe we didn't use it as much as we should.
"We want quality players coming off the bench and we had that up ton on Saturday.
“Maybe I should have played one of them but Promise wants to show what a top-quality player he is. He is a great lad who wants to be a winner.
Brown revealed that defender Darnell Johnson could be two months from first-team action after summer surgery.