Je me sens tenu de ...

[Crack1]

It is common to use the term that you are duty bound to correct something or someone.

Let us assume that I wrote some rotten French. You are a native French speaker or you may be a teacher of French.

When I make obvious or rather silly mistakes you could tell me ' I am duty bound to correct you.

1. Je me sens tenu de la prévenir .
I am duty-bound to correct her

2.Je me sens tenu de le prévenir .
I am duty-bound to correct him.

How about my French sentences?

[Frank]

Well, you really should use je me sens obligé de.

Se sentir tenu is correct and has the same meaning but it's really uncommon. People could even choke on it and consider it as a mistake.

It's more used as "Vous êtes tenus de..." (you must...) in formal texts, like rules and contracts.

[Crack1]

Of course it is fine to say that I have an obligation or rather I am obliged to ...

If you are an expert in French/English, it is very likely to use the words ' I am duty-bound to correct you'.

[Frank]

I'm not an expert in anything, especially not in British English.

But since, as you asked, we're talking about your French sentences, I can confirm that I've never heard nor read "Je me sens tenu de" in my whole life. You don't use "se sentir tenu de" when talking about yourself, or even when talking about someone in particular. This is something you might say while talking to a group of people, especially when reading company rules, school rules, etc. But not in other contexts.

So I just answered "how about your French sentences": you should use "obligé", not "tenu" in your sentences.