is currently upset with the both of us and won't stop bugging J asking "Why do you think I hate you?" Now I have to help J avoid T at all costs and T is also kind of a drama queen and most likely hates me now. I'm worried. But I really, personally, hate people you hate but think are you're friends when you've made it clear you hate them. And they try to bug you because they thing you're friends and they can get away with it kinda thing. So I wanted to help J avoid a situation like that but now I think I've just made everything worse for them...
Sorry for wasting your time.

Ahh, that sounds troublesome! I am so sorry! I'm not too sure what to do in a situation like this, but I feel like it would not be good for you to get too involved. This is a hardship between your two friends, and if they want anything to improve, they need to work things out and come to some agreement. That's not to say that you did the wrong thing - although what you said did have some consequences, at least you tried to help out. You showed concern for the both of them and did your best to join the broken bonds, so neither should be harboring any anger toward you.
I really do hope everything will turn out well; I'll be praying for you!

I don't think you should be avoiding T, but you don't need to talk to T either. Live your and J's daily life, and if T confronts you, tell T something along the lines of "We're not friends anymore because you're a selfish drama queen" but be sure to say that J has the problem with T - whatever that reason may be. Focus less on you, but not entirely on J. The result should be that T will lash out at J.
Now I say: You will hurt an ex-friend to protect your true friend. That is, if they truly are EX.

Hopefully this mind trick will get T to stop. But if you couldn't hurt T, then tell T something that will let them know you never wanted this to happen.

Note: This advice should be taken with a pinch of salt as I don't know your friends personally.

I'm mostly only commenting here because I've been in a similar situation, being the third party to another's souring friendship.
I don't like to be the type of person who puts his nose where it doesn't belong, but the only thing it takes for evil to prevail, is for a good person to simply do nothing.

That being said, assuming you ever read this, I might share some advice on how one might handle this should the situation ever arise again.

These things happen when lines are crossed. We tend to place lines as boundaries for our own responsibilities. In any relationship, be it family or friend, a 5O/5O responsibility list may seem logical, but in reality it leaves the other's 5O percent as a gap of anti-responsibility.

With a bit of creative thinking, this can be applied to many situations. For example:
If I am bothered by the habits or personality of another, treating that as their responsibility will not change my situation, only pull on some quiet tension until something snaps. On the other hand, talking with the person in question about what's bothering me, and asking if there's anything I can do to help make this problem less of an issue, helps the other see that I care, and want to mitigate problems.

Now, this isn't a as universal a fix as Duct tape, but one thing I do know is talking about our problems, as uncomfortable as it is, be the only way to really loose the tensions on the cords that bind people together. Just make sure to speak in a calm and meaningful msnor. Sharpness and raised voices invite self defensive retaliation.