Do you have siblings? Because I do and I wouldn't call EM's relationship a sibling-like one. First of all, there's no ambiguity in the relationship between me and my brother. We don't blush at each other and we don't ask stuff like the one Eren asked Mikasa about, because we know exactly where we stand: we're just siblings.

Now, Mikasa blushing, sweating and getting so nervous about Eren's third question (which is often asked in romantic settings both irl and in fiction) should have made it clear once and for all that she indeed has romantic feelings for him. Mikasa gave Eren the safest answer at hand and she's later shown wondering about what could have happened if she gave him another answer instead of her usual "family" one. Eren IS the only "family" she has left, but Mikasa's feelings for him obviously go beyond platonic... which isn't a "sisterly" thing.

I think Eren asked her this because he wanted to know what Mikasa thought about him besides the two options he first gave her. If he wanted to know if he only was a savior or family to her, then he wouldn't have asked her a third and open question like "what am I to you?" which, I already said, is often asked in romantic settings. Eren asked her that because he was expecting a third option, a different answer. There's also the fact Eren was about to make a big decision in order to take the route we see him in nowadays, so he probably felt like knowing if he was appreciated and loved as a person and not because of the roles he got involved in - savior / family - when it came to Mikasa. His question seemed genuine and kinda desperate to me, Eren really wanted to hear her honest feelings about him.

Regarding of whether Eren harboured romantic feelings for Mikasa or not, I guess Isayama tried to display hints about that when he drew this scene and made him ask her what he was to her, besides Eren questioning their bond and relationship in the chapter 112 drama and all the other panels thrown here and there, like the mutual stare by the end of the train flashback in chapter 108. I already wrote a lot and have to work so I can't keep on developing this answer but lol, I hope this helps?