I have to be honest with you: after two months with knee pain, turmeric with hot milk isn't going to be your main solution. That said, the curcumin in turmeric does have documented anti-inflammatory properties, but there's a problem here with dosage and bioavailability. Having a cup of golden milk at night probably won't give you enough of it for a real effect on inflammation. And well, I'm saying this from my own experience: a few years ago I hurt my back pretty badly on a camping trip where I fell while carrying heavy gear, and I drank that infusion almost religiously for weeks. It helped as a complement, but what really made the difference was a specific exercise program my physical therapist gave me.
What I'd do in your place is consult with a doctor or a physical therapist about that knee pain, because two months is quite a long time and it could be something that needs more serious attention. Turmeric with milk is a good option to take alongside other things, especially if you add black pepper (piperine helps your body absorb curcumin better), but it's not a replacement for a professional diagnosis. The supplements they sell in supermarkets now can have higher concentrations, so if you're interested in experimenting, maybe that would work better than just making homemade tea, but either way I'd start by ruling out something that might need rehabilitation or specific treatment.