I have had that same problem with both mine. Mine are also both sick right now and I have been doing that since last Thursday. I know it is frustrating at first and I get to be the mean Mommy because my hubby refuses to do that.
So, the bulb syringe-best thing to do as hard as it is. I use the little noses also. I have found that if I soak a q-tip with little noses and gently rub it in the nostril first, but not too far, just around the front to get the dried up and sticy stuff off first I have better luck. Then I get a really hot washcloth, but not to where it will burn them, and hold it loosly around there mouth and nose and let them breath in the steam. Next, I sit on the floor and lay them between my legs (sounds silly, but their head against my crouch area) put their arms under my legs and suction with little noses and bulb syringe.
I use the vicks cool mist humidifier and johnson and johnson soothing vapor body wash and lotion when they are sick. If you use a little of the body wash with the wet washcloth that works even better. And as bad as they feel and we know it will comfort them, we will not let them use a passifier when they are sick. From experience, it takes them longer to get better.