How can I deal with this better..?

[Lightsareonnobodyshome]

I work with a team who very much seem to work in silo around their own agendas. A short while ago a colleague confided in me about some struggles, which I confidentially supported but since then has pretty much reduced any conversation to difficult small talk.
There have been a few occasions where I have asked a question about an action or process which has resulted in a response which I can only describe as a verbal spit and I really don't know how to handle it. This happened again yesterday and then outside of the meeting, my colleague didn't seem to know where to look or what to do when she saw me, and as usual I just smiled and said good evening...
On the one hand I want to ask if there is a problem, but on the other hand I am not confrontational and don't want to turn this into something worse, but it really does upset me to the point where I think I dont fit and need to find a new job, which will be another challenge.

There is no need for them to be abrupt or rude to you, when you ask a question, there is no excuse for that.

I would let it ride and see if their same behaviour persists or if it was an off day or two.

If you get the sense they are deliberately treating you like that, while being friendly and cooperative with other people, I would wait until the next time they snap at you or respond to you abruptly and, in the moment suggest a quiet word. Then 'have it out' in a professional assertive way to find out if they have a problem because you've noticed a change in their attitude to you and don't want it to affect your working relationship as you both need to work together effectively.

If they don't try to sort things out, I'd leave them to stew in their juices, they're adult, if they aren't willing to deal with it, then it isn't your problem. Keep your distance and interface with them as little as possible. Don't be over-polite, i.e. trying to make a point, but be civilised.

Its work, its not adult daycare (although it frequently feels like it!).

It sounds like they've over shared some very personal information, I'd front it out and then assert when they are aggressive again.

Some people use private, sensitive information to force a relationship where there normally wouldn't be one - I wouldn't be surprised if they've had form for this previously, particularly if your new to the organisation.