I'd like to inject a little real science into this discussion. First of all, just because you're nursing your daughter (good for you!) does not mean that she will not get sick. If YOU have already been exposed to whatever she has and have antibodies against it, this will protect her. Unfortunately, viruses mutate very rapidly and there are many different types that can cause URI symptoms, so even if she has something you've been exposed to in the past, the virus could have changed just enough that it is not recognizable to the antibodies you pass in your breast milk. Also, if you're not sick with your child, your body will not produce antibodies to viral antigens in large amounts.
As for dropping breast milk into your daughter's nose, I've never heard of this folk remedy and would not think it likely to be effective for the same reasons as above. Further more, your body will not be able to detect viral antigens in your daughter by some kind of magical transference. Wireless works for Bluetooth and other devices, but not for immunology!
The funny thing is, anything you try at this stage is likely to "work" within the next few days. Most viruses run their course in 10 - 14 days, sometimes a little longer. What you do want to be on the look out for is a secondary bacterial infection, namely bacterial pneumonia. A recent study of over 19,000 children at a large pediatric hospital in Australia was just published in the prestigious British Medical Journal. The algorithm used by the doctors there to predict bacterial pneumonia in infants and children under the age of 5 years includes several clinical signs. If your daughter begins to show these signs, take her back to the pediatrician or ER ASAP:
Fever over 101 deg. F (38.3 deg C), especially over 103 deg. F. Very unwell appearance. Cough. Breathing difficulty. Slow capillary refill (press the pad of one of her fingers so that it blanches [turns white]. If it should return to a normal pink color in less than 2 seconds). Reduced or no liquid intake. Reduced or no urine output (a possible sign of life-threatening sepsis). Crying a lot.
I'm a little concern that she's lost her voice. If she begins to drool a lot and develops a wheezy, whistling sound, pack cool packs around her throat and get her to an ER as fast as you can. This can be a sign of viral epiglotitis, which means she's in danger of her airway closing.
As for allergies, yes there is a possibility of allergy to foods or pollens, but if she wasn't showing any signs of an allergy before, than this is not a likely explanation of her current symptoms. If there is a history of allergy in your family, it's certainly worth getting it checked out, however. One thing to keep in mind is that we're learning that general screening for allergens if there's no good indication can result in a higher rate of false positives. If you're going to test for allergies, try to determine if there is a specific trigger, and then test for that trigger. BTW, the most common allergens affecting children your daughter's age will come from food: milk, eggs, wheat, corn, tree nuts, peanuts and fish. Allergies to pollens and other inhaled antigens, such as cat or dog dander, cockroach feces, dust mites, etc., usually evolve following previous sensitization to a food allergy, and usually at a slightly later age (2 yrs and above).
BTW, most doctors DO know what they're talking about. That's what they spent 8+ years in medical school and residency learning. The problem is, they often either don't know how to explain medical issues well to lay people, or don't have the time. Remember -- your pediatrician sees hundreds of sick kids each week. You're dealing with only one. So, while you certainly know your daughters better than anyone else and should absolutely trust your instincts about how sick they are, your pediatrician is well practiced in figuring out what is causing the illness. You certainly don't want your doctor prescribing antibiotics if there's no need. This can only lead to bigger problems, such as antibiotic resistance, later on.
It's hard when your baby is sick! Do your best to keep her comfortable until the virus passes. Keep on doing what you're doing, and also try to keep her upright or semi-reclined as much as possible. That will help her breathe a little easier.
I hope everyone is feeling better soon!
I forgot to add that rapid heart rate and rapid breathing are also signs of a worsening infection, and, along with fever, warrant an visit to the doctor or ER.