Is welcomed used correctly in the sentence - my world and welcomed?

No, "my world and welcomed" is not a complete or grammatically correct sentence.

It appears you're trying to say something like:

* "My world welcomed [something or someone]."

* "I welcomed [something or someone] into my world."

You need to add a subject and a verb to create a complete sentence. For example:

* "My world welcomed the new baby."

* "I welcomed my new neighbor into my world."