Okay. You do need a bit more accountability here, OP. Yes, your mum was wrong to shout and scream at you. But her husband is dying and realistically, she won't be far behind. She's probably scared out of her wits and just wants to feel a sense of control over the situation. You should have handled that better. I absolutely understand the stress you're under, but you seem to think her shouting at you excuses your actions. There's a "we both did wrong but she provoked me" undertone to your post, and I don't think you can afford to think like that anymore. You're at the stage where it needs to become "she provoked me - I need better ways of dealing with that".
OP, your parents are both in their nineties. They weaker than you and dependent on you. Throwing stuff around and then walking out - by which I'm guessing you mean leaving the house? - will only have made your mum feel unsafe, at a time when she already feels vulnerable. It will exacerbate the very behaviour you're trying to prevent. I know it feels like clearing your head in the moment, but if you're trying to bring down the stress levels of everyone in the house, it's not the way to go.
On your friend: I understand why you feel like he betrayed your trust, but it does sound like you're not coping. He may even have thought telling him was a cry for help on your part. It sounds like he was trying to do the right thing. If he's been a good friend up to now, tell him you were hurt but you understand, and try to maintain the friendship. Caring is tough. You need your friends around you. Don't throw them out of your life unless you absolutely have to.
On the social involvement: I know, it's horrible. But maybe you could do with some help, and this will be a way to get you that. You may even have needed a bit of a wake-up call, so the situation won't escalate. I know that's a tough thing to hear, but the truth is you lost control here. The sense that someone is keeping an eye on you might help you stay your best self in future, and put the brakes on next time it all gets too much.
"I walked out": you haven't given much information on this, but if by it you mean that you left the house in a temper, and left two ninety year olds (one of them bed bound) alone, with no idea when you might return . . . I can see why your friend felt uncomfortable. Your parents are vulnerable now in the same way children are. I know it's an adjustment to see them that way, especially when they don't want to admit it, and when your mum still has such power to hurt your feelings. But it's true. It's time for a perspective shift.
Punishing them that way can't happen again. What if something had happened while you were gone? You'd feel awful. I know they're difficult, but there are better ways of dealing with them. Reach out. Ask for help. You can handle this. I know it's humiliating to have social services in your home, but they will have seen this kind of thing more than you imagine. It's a shit experience, but sometimes we need an outside perspective to open our eyes to the ways we're falling short. It doesn't mean the end of the world and it doesn't mean you're a bad person. Take the lessons you need to take from this and then pick it up and keep moving.
You can do it. You've already been a carer for so long. Think of this as just another stage you're moving through. Like childhood in reverse. Just as kids grow up and move from children to teens, and your relationship with them has to adjust, the same thing is happening now with your elderly parents. They're dependent, they're frightened, and they need your patience. You've become the parent now, in many ways.
This is a hard stage. But you will find your equilibrium. Things will settle. You've got this 🌺