You're upset because of a problem that you're having with your visa paperwork. You're talking to a friend and she can tell that you're upset. She asks what's wrong, but you don't want to explain your problem to her because it will take too long and you're too upset. You say:
I don't want to get into it right now.
To "get into" a topic or a story means to talk about it in detail. For example:
Jordan and I got into a long debate about whether to buy a Mac or a PC.
I'll get into that a little later.
The phrase "right now" sounds just a little friendlier and more conversational than just saying "now".
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