What tense is had been feeling?

This is past tense.

Explanation:

Had is a past tense word. If it was present it would say I am feeling.

quite an interesting way to teach topic sentences, because the answer to this question is the best definition of a topic sentence that one can present, it is as if answering the questions taught you how to do it, this is some real teaching, it is terribly well-done.

the topic sentence in this paragraph is:

topic sentences writers stay on track and keep a paragraph from becoming an aimless collection of sentences about an idea.

which incidentally tells you what a topic sentence should be.