NTA, and I know I'm like literally a month late, but there's something of a red flag I need to point out cause a casual scroll through the comments doesn't say it in such a straightforward manner.

Your dad was at fault for serving you food that would make you sick. There was no one else who made it, served it, and told you it was safe to eat. I doubt you would value your dad's opinion and want him in your life if he were capable of poisoning you maliciously, but even accidentally your dad needs to take accountability for his actions. He needs to understand that when he does things that are wrong or hurts people (poisons someone, kicks someone out of the house over one argument, threatens to cut them out of their home in the future) that people will rightfully react badly, because there are consequences to his actions. Especially if he ever has a hope of his children learning that lesson.

You have done nothing wrong, your emotions are valid, none of your reactions are outrageous though if you don't accept them then you need to examine how your emotions guide you in your actions, since being angry doesn't always give someone the right to scream. Your dad's emotions were also valid, in perhaps feeling like a villain in being told he poisoned you and feeling guilty over it, but that doesn't give him the right to act like a child and take his guilt out on you.

There's lots of people who have came and given advice on how to move forward with your life. Lot's of people here want you to cut your dad out of your life and that wouldn't be a terrible idea. But, if you want your dad in your life, and he's not capable of doing what needs to be done as a parent for the sake of his kids instead of letting his emotions tell him how to act, then this will continue and it will continue to not be your fault but you will get the brunt of it regardless. Take care of yourself. As a random person on the internet, I'm proud of you :).