Does this sentence need to second " to"?
" i'd like to talk TO you about my feeling"

Question

Answer

Yes, it needs the second "to".

1st to = infinitive "to"
2nd to = preposition "to"

Answer

Yes, you do need the 'to' after the verb. 
'Talk' can be both a transitive verb (takes an object) 'They are talking business.'
or an intransitive verb (doesnt take an object) Talk is intransitive when it means to express or exchange ideas by means of spoken words. When 'talk' is intransitive it is followed by a preposition, so we talk 'to/with' someone and we talk 'about' something.