a) Is it enough to study in a language school?
b) Is it enough to talk to your online teacher/language partner?
c) What is your story?
I've met people in non-English speaking countries that had native-like fluency to the point that they had English or American or Australian accents, and they had never left the country.
When I asked them how they got so fluent, their answers were that they were either married to a native speaker, or they worked or studied or hung out with native speakers (working in a hotel, playing in a sports team with foreigners, going to an international school...)
So I would say that actively interracting with native speakers on a daily basis is the key.
It would be easier and faster but it's not indispensable. I've been learning english for almost 10 years and I currently have a C1 level. Mastering a language took lots of time , patience and perseverance but if you pratice everyday you'll reach your goal.
I've been to London a couple of years ago for three weeks on a study course. It has helped me to acquire some new vocabulary and make more oral practice but that's it. I think it's definitely not enough to attend a language course because they usually teach you grammar structures and some specific vocabulary but you don't really have time to practice it which , in my opinion , is the best way to master a foreign language. You need to do a full immersion in the language you're studying. You gotta practice on a daily baisis( if possible) the 4 learning areas : listening , speaking , reading and writing .As for the speaking part you should find a native speaker to have a conversation with , it'll help you to acquire new vocabulary , idiomatic expressions and get the fluency.
Hope this helps
You don't have to go abroad but it's better if you can.
I've had really good experiences with language courses but only when they are intensive - five days per week for 4 hours and you'll be speaking a language in a few months. But this can be expensive.
If you can't go abroad or take an intensive language course you can also learn a language by yourself. I don't have super good advice on this, I've done it with variable success, but it's doable and it's up to you. In any case, even if you take a language course or go abroad I would advice to combine this with learning by yourself.
Try different things and see what works best for you. Study grammar, listen to podcasts, read, listen to music and look up the lyrics, talk to a teacher or a language partner. Do it every day as much as you have time and you'll reach your goal.