"I am not sure of who but you remind me of someone." (Do we need to use "whom" here?)
The way you have written it, yes, "whom".
"I am not sure of whom, but you remind me of someone".
I would drop that part however, and rearrange things a little bit for a more natural phrase.
"I'm not sure, but you do remind me of someone". Slight vocal emphasis on "do" as you speak it.
"I am not sure who [STRIKE]do[/STRIKE] you remind me of." [no question mark as this is not a question.] It means now I am asking that person "who does he remind me of?" Am I correct?
This means "whom" can only be used here, right?
I'm not sure what you mean by the last question. Your English teachers will probably tell you that whom is required in both sentences. Although some native Anglophones would use whom, most would say "who" in both cases. Nevertheless, you should write whom if you're answering a question on an exam.
I meant that I am asking that person [STRIKE]that[/STRIKE] "Who does he remind me of?"
No, you're not asking him that. You're asking him "Who do you remind me of?" It's a question that person is unlikely to be able to answer. Only you know who he reminds you of.
[STRIKE]Because[/STRIKE] I am confused so I am asking him like we [STRIKE]do[/STRIKE] sometimes [STRIKE]we[/STRIKE] ask others "Why is it happening?" We don't ask seriously, we don't expect them to answer the question. It's the same as [STRIKE]that[/STRIKE] "Can you tell me who [STRIKE]do[/STRIKE] you remind me of? Of Tom no I think of Tim." (The underlined part makes no sense. I don't know what you're trying to say.)
Perhaps you are talking about a rhetorical question.
John: You remind me of someone.
Jane: Do I? Who?
John: I don't know. I just can't work it out who it is.
Jane: I'm intrigued. I'd love to know who it is.
John (closing his eyes and banging his head in a frustrated fashion): Grrrrr. Who do you remind me of? It's driving me mad.
Jane: Oh well. Let me know if you work it out.
Tom asks Tim: "Who does Tim remind Tom of?"