That is an interesting idea and I bet it will help, but it's also important to remember that unless you've been told otherwise by a doctor, what you have is most likely just a common cold. It's a viral infection that the average adult contracts 2-3 times per year and the average adult contracts between 6 and 12 times per year. Sometimes, especially if you are under stress, a cold may last a week or two. The process of how stress suppresses the immune system is well understood and involves stress hormones like cortisol and other glucocorticoids. These hormones suppress your immune system when you are under stress because when you are under stress your entire body is preparing for fight or flight. It can't spare the extra energy to fight of a bacterial or viral infection, so it suppresses your immune system. Like your unconscious is doing in TMS, your stress response is actually trying to protect you.
If you've been having anxiety, insomnia and TMS, then you are probably under a lot of stress and it might take you just a bit longer to heal from a cold. That is completely fine and natural. The best thing that you can do is to stop worrying about the cough. Just ignore it.
Meditations like the one that Eric described might help if they help you manage your stress. Only you can tell if they are helping with that. Just ask yourself: do I feel more relaxed after meditating? Does it stress me out to have to add meditation to my already busy schedule? If both are true, which effect is stronger? If you find that meditation helps, there are a huge number of studies that say that, by decreasing stress, meditation helps to boost your immune system.
But, either way, a cough is just a cough. Unless it goes on for several weeks I wouldn't even worry about it. Just go see a doctor if you want to rule out anything serious and then just relax knowing that you are fine. Doing this will help with your anxiety, your insomnia, and all of your other TMS symptoms as well!
