Sounds like you might have picked up an injury.

Physical therapy is recommended if you have access to it - a good physical therapist will be able to identify the root cause of the injury and recommend a specific treatment plan to mend it and prevent it from recurring.

I'll add that spending some time on weight training to help strengthen the body in general may help reduce your injury risk, and is a good idea for general health in any case.

There's two main culprits for runners knee.

If you have suddenly increased the distance you run, you may need to ease back, and do a gradual increase instead, which gives your muscles and soft tissue time to adapt to your increased load.

Otherwise, it's often a gait issue. Ankles that roll inwards or outwards too much etc can cause torsion pain. In this case, it means better shoes, and ideally, shoes that address the issues with your gait. The thing about gait issues is that in the day to day, we don't even know the imbalances are there, but when you start running a lot, the increased strike rate and strike strength means issues can start to show up. In my case, I need shoes with support that stop my left ankle from rolling inwards.

which only worsens if I don't rest

Sounds like you need to rest.

Jokes aside, you actually need rest to progress. It doesn't hurt to take a week off or skip a run or two to recover. Slow down your mileage ramp up too. Slow progress is still progress in the end.

By the way, in terms of knee pain specifically you may find that changing your footwear and/or running style can alleviate it. Landing on your heel puts a lot more force through the knee joint compared to landing on the middle of the foot. Traditional running shoes are designed to land heel first, which is why they have so much cushioning, but you can buy lower profile shoes that allow you to run differently. This will redirect load to your calves, though, so you'll likely need to strengthen those before being able to run whatever distance you're currently comfortable with.

Back when I ran 40-60 miles a week I found I needed to shift to a more supportive shoe. The PT and the doc essentially said the my shoes did not give me a push back when I was running. I switched to a Brooks Beast and my knee problems went away.

I developed intense knee pain one day after running. I had been sick for a few weeks and went back to my regular routine and after my 20 miler of the week I found I could no longer walk up the three steps to get into my house. It isn't that it hurt so much but that my knee felt weak and unstable. I sat and layed in front of my steps for a few hours until I could get up enough to unlock my door. In that time, I decided I was weak and just needed to cut back mileage for a couple of weeks. I was wrong. It's about ten years later and I still can't run more than 9 or 10 miles without a week of prep first. I saw doctors, PT and hippies. Pain relievers and muscle relaxers helped but made it hard to keep my cadence. PT gave me stretches and a resistance band and told me to do exercises for three weeks before trying a short run. The hippy gave me some RC that was kind of like acid. I wish I had just listened to the PT. The IT band stretches ended up relieving my pain and made it so I could reliably go up stairs again. I recommend seeing a PT or sports med guy and doing what they say. Otherwise, for me it was IT band stretching and switching to zero drop shoes. Good luck, get healthy and stay there!

You can treat them with RICE. Rest, Ice, Compression, Elevation. The most important thing is to not overdo it in the first place, though. If you are regularly encountering pain after running then you are pushing your body too hard.

Easy.

Don't run. Running is for bomb-technicians.

Bike instead.

Less running. More Rest. Pain medication. Ice.

Foam roll! Most knee pain in my experience is from tight / twisted muscles in the upper leg. Just make it a habit to foam roll every single day.

Have you tried shoes?