I know it is hard and some awful people can be mean about it. Try to surround yourself with supportive people who will help you and switch languages when you need them to.
One thing to try is to write down questions in English and read them out. Over time, you will get better. But until then you won't lose out on participating. And people who see you trying will help you and cheer you on.
The advice about an hour of conversation every day in English is great. It'll get better over time.

I can read, comprehend, and write sufficiently well. Usually, I don't need any assistance. The problem is with conversational skills.

I can't speak in English with fluency. There is always a conscious effort to converse in English. There is no flow like other students.

Just keep speaking in English with everyone you can, particularly with the kids from metro cities who speak English like it'a their native language. You will initially stutter, feel embarrassed, struggle to keep pace with your friends, but within weeks you'll catch up with them. From what you've written I can see that your grammar is decent, you only need to build confidence with your spoken English. I shifted to a city-school from rural MP and like you I had the grammar but not the spontaneity that is needed to converse. I kept speaking to kids in English and took part in every conversation I could. I could feel an improvement in my speech within a month.

Find someone who understands your plight and doesn't condescend you for this( maybe a batchmate or a senior with whom you are on friendly terms). Ask them if they can chat with you in English for maybe an hour daily and help you out with enunciation and spoken english. I know it will be tough to find someone, but people in their 1st year are more willing to help you out and be friendly as compared to them in their later years of law school (competition sours friendships / general relationships).
Try and put yourself out there and practice speaking daily. Its scary but it will eventually help you in conquering your fear. Plus there are more people that might be going through the same problem, its more common than you think. Find them and practice with them. Don't be debilitated by it, its pretty normal and even if in the end you aren't as fluent as your peers, it won't make a big difference if you are solid with your grades and extra curriculars plus legal know-how.

Focus on what you are trying to say, as opposed to how you say it.
Content is king.
Confidence matters. Learning a language is just like exercising a muscle. You have so many resources available to you online and if this bothers you, devote at least 30 minutes every day for this. This isn't something you lose sleep over. You have every right to be there and you can achieve great things with what you have.
I know, because I was you when I joined.

I have done my schooling from a not-so-great school. It was an English medium for namesake. There was no emphasis on conversing in English. Neither anyone focused much on those. In fact, talking in English was something looked down upon in the circle.

Now, I am here in a law school. Everyone now and then, I feel insecure. I have no fluency - I take a pause to choose the appropriate word, I stutter, and what not!

I feel so frustrated.

How do I fix it? I still have no one to talk to without embarrassing myself.