Is it a necessary for a Linkng Verb to be an intrasitive verb.

For Example. Take the verb "feel".

1. The blanket feels soft, warm and comfortable.

2. The child felt the blanket.

Linking verbs are not always considered intransitive verbs (there are generally 3 types listed: transitive, intransitive, and copular); but they do not take an object-- when acting as a linking verb. I say this because your examples are of a verb that can be either transitive, intransitive, or copular, depending on the meaning:

I feel my nose.
I feel for you.
I feel hungry
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Wonderful examples!
Sometimes the verb "feel" is intransitive, as in "I feel bad." In this case, it is a sense of being, not a physical act of touching something. Therefore, you would use the predicate adjective "bad" as opposed to the adjective "badly." This is a very, very common mistake.