If you can safely practice inversions like headstands, shoulderstands, and handstand, those are great when you're sick; your lymphatic system lacks an organ analogous to the heart, so lymph doesn't get actively pumped around the body like blood does. It just kind of seeps around, moved primarily by the action of skeletal muscles and joint flexion and extension.
Inverting for a few minutes is a good way to move lymph around, which is extremely beneficial for the immune system.
If you don't practice inversions you can still get a lot of that even just by lying on your back with your legs up a wall. Anything to reverse the flow of gravity and get that lymph flowing.
But inversions like head & hand stand will also throw some muscular work in the mix too.
If you're super stuffed-up, though, when you invert if you feel pressure building up in your head, come out, as that's not good, you'll end up with a bad headache. Instead, then, you can stand with your back near a wall and just do a forward bend, try to touch your toes, relax your neck and let your head hang loose, hold your elbows with your hands so your arms can just hang down too; that'll do a lot of the same stuff without making it feel like your head's gonna explode.
As for neti pots, it's basically the exact same thing NYC's talking about with the squeeze bottle. You want to be careful with too much pressure, don't want to hurt those mucus membranes. That's also the reason to use an isotonic or slightly hypertonic solution (i.e. as salinated as your tissues, or even slightly more), so it doesn't irritate those mucus membranes (they're already pissed off at you enough.)
Jala neti, as the practice is called, has 3 stages. In the first, you pour water in one nostril and let it drain out the other. In the second, you pour water in one nostril and gently sniff it into the mouth and spit it out (this is trickier, as it's easy to accidentally swallow the salt water instead.) In stage 3, which I've never even attempted, you take the water into the mouth and release it through the nose. I don't even really know how I would go about doing that.
Stage 1 (in one nostril, out the other) is definitely useful, but stage 2 gets a lot more out, and I need to do both when I'm congested or I still can't breathe through my nose.Here are some detailed instructions
, although I don't snort water out of a bowl for stage 2, I tilt my head even more upside-down and keep pouring out of the neti pot.
Also, at the bottom there they discuss a practice called Sutra neti, and even looking at the photo kind of makes me a little queasy, so be warned. :)