In this case, do is an auxiliary verb that replaces the verb feel that is mentioned earlier in the sentence. This is a common thing for auxiliaries in English. Thus, your sentence can be rewritten as follows:
I don't feel like I usually feel.
That's what it is actually saying. So, your interpretation is wrong.
Compare your example with this short dialogue:
— Do you feel like you got the answer right?
— Honestly, I don't feel like I got it right. / Honestly, I don't feel like I did.
What we have done here is replace got it right with something shorter, namely did. The auxiliary verb did tells us two things: what happened is in the past tense and the information about what actually happened is mentioned somewhere earlier in the dialogue.