"My eyes hurt because I looked at the computer a lot."
たくさん is valed here. You could say a symilar thing with 見すぎる, but the meaning it a little different. たくさん見て is "to look a lot" and 見すぎる is "to look to much". I do think useing 見すぎる would be more normal and would probably be better to use, but i don't think duoligo expects us to know that grammer at this point.