Toddler Waking at Night, Sometimes for Hours

Welcome to sleep training a toddler!
It's much harder than babies, since little personalities are involved. But basically, you need to start from scratch.
Choose a method to extinguish the behavior. Whatever your comfortable with. But recognize that how YOU respond to him overnight will dictate how long this lasts, and what he continues to do.

He's waking up and screaming because he wants you to go in there, and you are. Totally understandable when he's sick. But now it's time to reset the message that night time is for sleeping.
For mine, at that age, he got 1x that I would go in. (I could tell if there was a bad dream involved.) Beyond that, I tucked him in, told him I wasn't coming back until the sun came up. Took a few nights of crying it out to get back to sleeping again. But he got the message.

I second the last opinion. I go through this every time after the little ones are sick. It takes a night or two (or three) to get them back to bed on their own. But what can you do? When they are sick they need the comfort. But you have to get back to a routine for your sake and for his sake. I wish you the best of luck. Hang in there. Now is the time to be consistent.

If he's up for hours, it could also be that he's at an age where his nap schedue needs to be adjusted. I'd say give him his nap earlier. Also, when he wakes, for now go in and comfort him but without picking him up.

What about introducing a new stuffed animal named "Sleepy Sam?"
This 1 particular stuffed animal can accompany him for the bedtime story and for bedtime.
Keep the bedtime routine consistent. Realize that it does take a while.
I used to have to tell myself to stay calm. Otherwise, my daughter would sense the impatience.
I do agree that he will need to get himself back to sleep.