If I died, what is kept when I enter heaven?
The essential 'you'.
In traditional Jewish/Christian thinking, the body is the manifestation or form of the soul in the physical world. Soul and body are one in that regard. There is a persistent non-Abrahamic dualist influence which tends to see the soul and body as two different things, as if a soul inhabits a body, but this has consistently been resisted by orthodox teaching. There is discussion of 'body and soul' in terms of the flesh and the spirit, but this addresses a subsequent aspect. It's important to grasp the first point first, and then the second accordingly. Sadly this is not often the case.
Who am I anyways, if not constantly defined by struggle?
The struggle is not who you are. The struggle is what you contend with. Why you struggle says more about who you are.
'Who am I?' is a good question, but it should always be regarded in a dynamic sense, or a sense check question, rather than looking for a definitive answer. There is no definitive answer, because our self-knowledge is always insufficient, because we're not a 'closed' entity. When one arrives at the point of saying 'I am ...' all further progress stops.
How can that even be "me"?
Well the struggle isn't you. If the things you struggle against went away, where would you be?
Am I not really who God wants me to be in my current form?
According to every tradition, no.
Am I simply a little part of God?
'I am a little bit of God' is like saying 'I am a little bit pregnant', whereas in both cases one either is, or one isn't. If one is God, then one would know, as God knows ... because one doesn't, it's safe to say one isn't.
Or do I need to study more of the Qur'an/Bible?
Well it never hurts. Of course study without access to commentary is a bit like trying to follow a map, at night, with no lights, no compass ...