Not an uncommon experience.

Curdled milk results from the level of acid in the milk becoming higher than normal (which makes for a lower pH level). At normal milk pH levels, the protein molecules repel each other. As pH goes down (acidity goes up) curdling occurs when the protein molecules no longer repel each another. Heat speeds up this process considerably. When milk goes sour it's due to growth of bacteria that produce acid as waste. There can be a small amount of acid from minor amounts of bacteria, not enough for the milk to taste off or to cause harm, but enough to curdle when heated. An example of is when one has sniffed the milk and/or tasted it to ensure it's ok and it's fine, yet a minute or two after pouring, it has curdled in one's coffee or tea. Depending on nose sensitivity and levels of acidity, one may or may not notice a slight sour smell in the rising steam.

Back to your issue: If you drain those curds you'll have cottage cheese. Keep refrigerated and use fairly promptly--I've been told 3 days but when I've stored it in a very clean glass container like a mason jar with a new lid, and at no more than 40F (4C), I've had it last 7 days or longer. Should you find the flavour too tangy, wash the curds again (or twice more) in water and re-drain. Can be drained by gravity by hanging in a muslin bag or put the bag in a strainer and put weight on top (use plate to fit just inside the strainer with tinned food on top). When drained under weight the result is firm enough to slice, as in paneer or tofu. I'm not big on making cheesecake so I can't say which drain method is best for that. I can, however, say that the cheese is yummy with a bit of added salt & pepper, fresh or dried herbs, and an optional jot of flavourful oil like olive or sesame, spread on toast or bread or crackers. Mmmm... Or mixed with bread crumbs & basil to top baked tomato halves.

For my favourite drainer strainer I made a fitted muslin liner by sewing darts into a flat piece of tightly woven muslin--put darts to outside when using. I find grocery story cheesecloth to be silly--far too loosely woven and not wide enough. My strainer nicely fits/accepts a pot lid instead of using disposable plastic wrap. I prefer a strainer to bag hanging because draining can be done in the fridge, which I figure helps with shelf life.