Usage of verb ADD

Hello, How do you feel?

My question:

I?ve always used this verb to mean “put some
more, for instance, sugar in a coffee”, or
in Maths.

But, I am not sure if I can use it in direct
speech when someone wants to say
anything else after having said something
before. Do you use other verbs?
Which ones?

My example:

“Don?t worry!”, the doctor told me. “It takes
just a minute”, he ADDED.

Is it correct?

Thank you very much!

Jes?s.

.
Your example is fine. Interlocutors can always add their comments to a conversation-- so others can add as well as the first speaker.
.