With all due respect to your approach to your child's illness... she is quite young, and you first need to have a diagnosis, to see what is wrong with her. THEN, that way, a remedy can be suggested and implemented.
Bear in mind, that this has been going on for 2 weeks, with nothing helping or 'curing' it. Since she is a young baby only 6 months old... you need to make sure she does NOT have some kind of infection, or bacterial infection. If untreated, it can get worse, affect her lungs or damage it etc.
She seems very congested. There are a variety of reasons for coughs/congestion like this... which only a professional can determine. And, Pneumonia can be a complication, sometimes, in illnesses like this. And it can be dangerous and the child can end up in the hospital. THAT would be my concern as a parent... and that she has been this way for at least 2 weeks with no improvement.
Here is a link on coughs, in babies as an example:
Using guesswork and giving things to a baby, can also pose a danger or a risk. Because you don't really 'know' if it is safe for a baby. Especially at that age. And then meanwhile, it could or could not make her condition worse. Meanwhile, trying things and then waiting to see if it works... takes time... and meanwhile, her condition can get worse. To me, time is of essence too. Do you just wait and see if it gets better, or do something specific that you KNOW will work and is pertinent for her illness or infection? PLUS, at this age... many foods are not appropriate for this age... and you could get another complication, if giving her something that is not yet appropriate for her age and physiological development and digestive development.
I think, there are too many "what if's" and guess work... to appropriately address her illness. Namely, she has not been examined, AND there is NO diagnosis on her condition... so 'treatment' cannot be further applied, correctly.
I certainly hope, she does not have an infection of some kind, or a secondary infection. Does she have fever? Is she able to breathe? Is she getting enough oxygen in her? Babies this age cannot often 'know' to breathe through their mouth yet... and this can really affect them. Is her skin normal colored, or turning bluish? If her skin color is not normal this can indicate that she is not getting enough oxygen in her bloodstream, for example. This is dangerous.
At least she is still nursing. Because you don't want her to get dehydrated. This is also dangerous in a baby. Is she having enough wet & poopy diapers? If not, this can also indicate dehydration.
There are so many possible guesses... but only the appropriate solution will help her. But first, this will depend on getting a real diagnosis.
As an example: my Mom was once sick with congestion and coughing. She did not want to see a Doctor and just took natural things and let time 'solve' it. She too did not want "medicine." Well, after a couple of weeks it did not get better, she had a hard time breathing too, of course. She FINALLY went to the Doctor... and by then, she had developed bad Bronchitis and almost Pneumonia. The Doctor said she needed to be in the hospital, which she refused. Meanwhile, because she did not get her condition properly treated in the beginning, she had developed PERMANENTLY damaged lungs, and now has a benign abscess in her lungs now. NOW, her lungs are permanently weakened.. .and whenever she gets sick, she has to be EXTRA careful she does not get any secondary infections. AND, when she gets sick now, she also develops asthma. She learned the hard way. But her lungs are now forever 'sick.' If she had not gone to the Doctor, she could have even died, because she had walking Pneumonia by then. She didn't know and just thought it was a bad cold. Very sad. She is elderly.
For the elderly and young babies... their bodies are not as adept at fighting things off... and it is very important to properly treat these ailments. Even if just to make sure it is not getting worse or affecting the body, negatively.
I don't have any answers for you, but just some thoughts.
All the best and take care,