Is it always right to help others?

No, not always. Most of the time, of course, but not ALWAYS.
Let me address some of the times where it is NOT right.

To be clear, in what follows, I’m not talking about the trivial &/or the occasional situation here, but the important &/or the repeated.
Neither am I talking about when dealing with very young children or the physically or mentally incapable adult.
Neither, of course, am I talking about helping people to do something that you clearly know or believe to be wrong.

So, caveats over, I propose the following:

Do not do for someone else anything they are capable of doing for themselves.
If you do, it’s a form of theft, since you are taking away their agency and imposing your own.

Don’t make a dependant out of someone else.
Don’t decrease their possibility in life just to exercise your own or to make yourself feel good.
Don’t remove their purpose, their agency, their ability & responsibility to act in a meaningful way in life.

Be an enabler to their agency, their blossoming, their Being, not an inhibitor.

Teaching &/or doing things for someone are not exactly the same as enabling.
Enabling is about giving them the tools and encouragement to learn how to or actually do things for themselves.

This is so hard, particularly with your children or frail elderly folk.
You care so much; but it’s not about fulfilling your desire to care or to be a knight in shining armour, it’s about what’s best for them.

Don’t pretend to yourself that you are a caring person unless you always centre the other person’s best outcome, not your own, and consider more than merely the immediate-term.

The child must learn resilience, self-sufficiency and to cope with failure at some point.

The frail old person must still feel useful; feel capable at some basic level; still have a reason to be here. Don’t take that away unless there’s absolutely no alternative.

Say things like,
‘you can do that for yourself. Have a try and then I’ll help if necessary.’
OR
‘see if you can work out what to do. Have a go. Ask questions. Don’t worry about getting it wrong. Making mistakes is how we learn. I’ll be here to answer questions, to guide and help you, but only when you’ve tried yourself.’

In the end of course, it’s about judgement of when to help and when not.  
Good judgement comes of wisdom.

So just make sure that you’re making that judgement having carefully considered what’s best for them, and realising that what's easiest for them is not necessarily what’s best for them, and at the same time, what's easiest or most advantageous for you, is also not necessarily what’s best for them.