I think it's the same if you want to say in English 

in Russian it's different btw

how did you feel - nervous or comfortable 

or what do you feel - I felt myself uncomfortable (for example)

isn't it the same?you just use different construction of sentence 

I think it's more commom with "How". If you ask with "what", you'd have to answer always with a substantive.

Ex: I felt sadness or I felt happiness.

I felt embarrassment.... etc... :)

For example

"What do you feel..."  ans: anger  (emotion or maybe an object)  

"How do you feel..."   ans: angry (emotion)

This is my opinion : )

Jose is right.

The usual question is 'How did you feel?'. This is is asking for a general description of your feelings.

'What did you feel?' requires a noun* as an answer, for example 'fear'.

* Note that the part of speech is called a 'noun'. We don't use the word 'substantive'.