"I've got into a very difficult situation" suggests that the situation is unresolved and you are still seeking solutions to the situation. "I got into a very difficult situation" suggests thas the situation has been resolved and dealt with, the situation is in the past.

I've got into a very difficult situation. —> Sounds more like how an English person would talk, actually, than an American. It sounds very passive. "I've got into a very difficult situation" would mean that whatever situation happened in the past but it is still affecting you. I got into a very difficult situation. —> The situation happened in the past. "I'm in a very difficult situation" sounds more normal for a present situation. Or "I'm in a very difficult position"

I've = I have I have got into a very difficult situation. (in the past) I got into a very difficult situation. (just now)