I'm not a doctor (well not the MD type at least) but commonly sick with respiratory problems so I see MDs a lot.

I put in the source the Medline Plus note on nasal discharge. Given that you have a head cold you have sinus blockage which restricts the natural discharge of the mucous. Lots of fluids is your first step. I highly recommend nasal irrigation. The Mayoclinic demonstrates what it does and the medscape article talks about efficacy.

You can get a cheap plastic nasal irrigator from your pharmacy. It is definitely about low-flow (minimal pressure) and gentle flushing of the sinus cavities (hence saline solution). Definitely do NOT use anything high pressure like a Waterpik. One reason I find it useful is keeping the mucous from dripping down your throat. Also frequent flushing gives you a sense of changing color and amount which tells you if it is clearing up or not.

Hope you feel better. And of course consult your doctor.

I'm certainly not a doctor, but I think I might have an idea what's going on here.
Usually the brown tint in bodily fluids comes from blood. Though blood is red, as it dries and oxidizes it becomes brown. If you have a sinus infection, the mucus will often be bright green.
I'm guessing it's winter where you are, and with the air getting dryer, most people suffer from dry and itchy skin, which also means the inside of your nose can get rather dry and cracked - I'm actually going through a similar thing right now where both sides of my nose are bleeding a little bit - only noticeable when I blow my nose. I get it every year and it's a PAIN, because it can take WEEKS to heal. Add that to the irritation of blowing your nose with a cold, and you've got a little cut or crack inside your nose that just refuses to heal - basically, you've got a constant nose bleed that isn't being allowed to heal.
The question really is how much of it is brown - if it's completely brown, paired with any sort of sinus pain, and thick, sticky mucus that is difficult to move, you've likely got yourself an infection. Though most people exhibit infection though bright green - yellow, brown, or grey can also signal an infection. IF it's just streaks of brown in normal mucus, it's more likely to be a cut.
Most of the time, you can get over it by just waiting it out - don't blow your nose too hard (which will irritate it), it's often a bad idea to take medication as (your right) it can thicken your mucus, which is not really fun for an irritated nose at all. You may also want to try a humidifier - if you don't have one, getting a bowl of boiling water and simply breathing the steam will also work - a sauna (though they're often discouraged if your sick), or, my personal favorite, steam up your bathroom and (given it's clean), take a nap or read a book. It'll soothe your nose from drying out so much - some vicks or something may also help, but limit it's use because it can become drying after some time.
You likely don't need to head to a doctor or anything - MAYBE if you have a lot of sinus pain, but even then, you can likely get over it on your own.
Good luck, and feel better!