I (16) live in a residential unit. I have a very strict curfew. If I am late I am grounded. Is that right?

Your carer in the residential unit has to look after you.
That means that you are not allowed to stay out too late.
It is right to say to you:
You must be home on time in the evenings.
However, you have the right to have fun with your friends.

Sometimes you may lose track of time.
You come home much later than agreed.
Then it is right if your residential unit is stricter with you.

However, sometimes it is not your fault that you are late.
Because the bus is late.
Because an appointment lasted longer than planned.
In that case it is not fair that you are punished.
Your carers must take this into consideration.

Being grounded may not be fair.
If you think you are being treated unfairly then you can seek help.
For example, you could talk to your guardian about the matter.