"I am confused" means "I do not understand."
From The Free Dictionary:
confused [kənˈfjuːzd]
adj
- feeling or exhibiting an inability to understand; bewildered; perplexed
"I am getting confused" has basically the same meaning; the implication is that they are in the progress of becoming confused ("I'm beginning to not understand").
A more common phrasing this (in my experience) is:
I'm starting to get confused.
This is a polite way of saying you've strayed into an area that they don't understand, and would like you to explain it differently or perhaps slow down. This also carries the implication that their confusion began recently; for example if you've been discussing something for an hour it's safe to assume that they're not confused about everything you've said, but that something you've said recently has confused them.
To address the source of your misunderstanding:
You mentioned that your guess as to what "I am getting confused" meant was "somebody thinks I am somebody else." If you actually want to say "somebody thinks I am somebody else", you would say:
I am often confused with Michael Jordan.
The with is very important; when you are confused with someone else, that means that very often people think you are that person. If this is something that has happened only once, not as a recurring pattern, you could say:
She confused me with [x].
Or if the event is still occurring, you could say:
I am being confused with [x].
Though this is unlikely, because usually if someone mistakes you for someone else, you clear the matter up immediately (that is, you'd tell the person they're wrong and the confusion would end before you would turn to someone else and tell them what's happening).
I agree with JR – it means about the same as 'lean on me'. Also, there is a subtle second meaning that is, 'don't resist me'.
For other ways this versatile phrase can be used, check out Sheryl Sandberg's TED talks where she uses 'lean in' in a business context.
Best Answer
To be lean on feelings means to be low on feelings.
Similar to my car is getting lean on gas (it doesn't have much gas left).
If things are lean, it means "they are very low, or kept as low as possible." (Cambridge). This is how lean (on) is used in this context.
This is why the character says I can't afford them. In the present situation in the movie, he cannot "afford" [to have] feelings, so he keeps them as low as possible. (There might be so much trauma going on that he simply cannot afford to have many feelings and remain sane or be able to act in the current situation, and as I recall the movie is about a Soviet invasion of the USA.)
There are two other idiomatic uses of lean on, neither of which fit this context:
1 to depend on something or someone (He leaned on his father all his life.)
2 to pressure someone (They really leaned on me to pay back the money I owed him.)
Of course there is the straightforward meaning of lean on, as in
He leaned on the wall while he waited for his turn.