OP's first suggested meaning would be correct if we just discard the word "offer"...
I feel helpless = I feel as though I am unable to help [myself, or another, depending on context].
OED's first two definitions are...
Destitute of help; having no assistance from others; needy. (Of persons, their condition, etc.)
Having no resources in oneself; unable to help oneself; shiftless. (The ordinary current sense.)
...from which you might reasonably suppose that feeling helpless is always and only concerned with your inability to resolve your own problems. But in practice if you're with someone else who has a problem, and you can't resolve that problem for them, it's natural to perceive yourself as having a problem of your own (that of being unable to deliver the help someone else needs).
In short, helpless means powerless to do anything helpful - in respect of your own or someone else's problem, according to context.