I am looking for a word for someone who feels like they need to be admired. By this, I do not exactly mean someone who is convinced that they are a supreme being, and need to be worshiped, or something like that. I just mean someone who maybe is slightly insecure, and feels like if they need to be looked up to by others to feel important. I know this is a bit specific. Is there a word for this?
Perhaps you are refering to someone needy. According to Collins:
1) in need of practical or emotional support; distressed
Extrovert, show-off, attention-seeker... self-doubting,
I think a psychologist would probably write something like
the patients self image is derived from there perception by others.
I'm struggling to think of any synonym that doesn't seem to have unkind connotations though.
perhaps something like unloved, unvalued, neglected
If the person in question only needs to be admired, "narcissist" is probably the word you want. As an aside, the word for the type of person who believes himself deserving of worship is "megalomaniac".
In the New Yorker article "The Shape of Things to Come" about Jonathan Ives, chief designer at Apple, Steve Jobs is said to have called this vanity, the trait of a vain person:
Jobs’s taste for merciless criticism was notorious; Ive recalled that, years ago, after seeing colleagues crushed, he protested. Jobs replied, “Why would you be vague?,” arguing that ambiguity was a form of selfishness: “You don’t care about how they feel! You’re being vain, you want them to like you.” Ive was furious, but came to agree. “It’s really demeaning to think that, in this deep desire to be liked, you’ve compromised giving clear, unambiguous feedback,” he said. He lamented that there were “so many anecdotes” about Jobs’s acerbity: “His intention, and motivation, wasn’t to be hurtful.”
Now, I happen to think that believing your "acerbic" criticism is always so wonderfully constructive is an even worse vanity. But in the vein of the OP, a person who needs some sycophants or bootlickers is, as Steve Jobs put it, vain.