I don't think this has anything to do with Shia or Sunni. It has to do with political landscape of a country. Azerbaijan, as far as I know doesn't have sectarian problems. Matter of fact, I personally didn't even know the majority of Azerbaijan was Shia until a couple of years ago. And when I did find out it didn't affect my opinion about Azerbaijan in any way, was just surprised that I didn't know that. But just goes to show how much of a none issue this Sunni/Shia thing is.
But I'm afraid it is a problem in Iraq itself and and regions like Yemen due to Iran's foreign policy. Iran is or wants to be ambitious with it's foreign policy and wants to widen it's sphere of influence. Currently they can control only or mostly Shia groups outside of Iran, and this leads, willingly or unwillingly to sectarianism in the region.
Your last sentence: "...just like to show our Sunni brothers that we're brothers and we want to be United but they never showed any same gesture alas". This last sentence, even though you want to to show Sunni's that you are brothers and want to be united, still take a jab at the end by saying that they didn't show the same gesture, kind of putting the blame on them. I'm sure there is a Sunni somewhere that uses the exact same sentence by the way, it's not to call you out or anything. All sides are doing this, and that's why it is still a problem. If everyone started to put the blame on themselves and tried to figure out what they themselves were doing wrong, and simply trusted each other and accepted each other for who they are, there wouldn't be any sectarianism. And external provocations wouldn't have any effect on anyone, no matter how hard they tried.
Lack of trust, acceptance etc. reflects in the fact that Iraq has all kinds of different sectarian or ethnic militia's, that's kind of a statement that there is no trust and acceptance between the different groups and I'm afraid it's only a matter of time till these millitia's will start fighting each other or be a catalyst to other kinds of conflicts (InshAllah I'm wrong about that). In my opinion, Iraq should only have official governmental army's.
But that is just my opinion as an outsider looking at the issue, I'm sure you have more knowledge and better understanding about this whole thing, so feel free to correct me if you feel like I made a mistake.
This is a personal story but a long time ago, I asked my Imam (of a state organ Diyanet mosque) about what Shia Islam was. And he gave me an example, he said imagine a highway with 4 lanes (the 4 Islamic schools of Sunni Islam; Hanafi, Hanbali, Shafi'i and Maliki) and that you switch lanes if the situation calls for it. But in some situations I could even switch to a secondary highway (Shia Islam) which has different lanes as well, and that I could specifically use the Jafari way of Shia Islam.