No, you just need more practice with a native speaking tutor who can correct you as you talk. If you asked the above question to a tutor, they would correct your grammar for you and you would know not to use the word 'well' in this sentence. Dont worry too much about grammar rules, it is better to learn through practice.

There is a huge difference between "using grammar correctly" and "knowing the grammar rules and being able to explain them". Native speakers use grammar correctly because we pay attention and listen (and yes, we are constantly exposed to proper examples). Yes, you can do this too. If you approach grammar as technical knowledge but without practical application, you will only be confused by the numerous rules. I see some learners speak English badly because they focus too much on rules without understanding those rules properly. So, follow the good examples first, then look at grammar in retrospect. Don't ignore it entirely, of course. I suggest looking at Alex's corrections - they are good examples of the right way to ask your question. Another possibility is, "Do we need to learn more grammar to speak English well?"

Certainly you do, for "well speaking", But if you just want to be understood, then probably no. You'll note that all these didactic people had no problem understanding your question.

Not answering, but just correcting your question: "Do we need more grammar to speak better in English". Or "Do we need more grammar to be able to speak better in English."