My 4 month old baby is coughing & sneezing

I noticed that my baby started coughing two days ago. I think her cough sounded dry. I thought at that time that maybe it was partly due to her saliva. She seems to drool a lot and everything she grabs she puts in her mouth. Also, I think she even wants to suck her whole hand ^-^

The very next day she was quite fussy and seems irritated. I was not sure what's wrong. I thought that her mood must have changed since she's already 4.5 months old. But then she seems to have difficulty breathing because of her cough. I didn't know what to do. It was really hard for me to see may daughter that way. I got panicky.

My husband's relative flick my baby's tummy with her fingers. It made an odd sound. She said that "may kabag si baby". I was confused since I burped her every after feeding. So, we just applied "manzanilla" on her tummy, soles of her feet, and then at her lower back. 

Today, I noticed she coughs and sneezes at the same time. Also, she seems to be coughing up a clear sticky like phlegm. She even vomited once today and twice yesterday. I constantly check her temperature ... Buti nalang, no fever at all.

I would just like to share what my baby's pedia prescribed:

Sinase - 2 nasal drops, 3 times a day (I hold her in a burpin position then after a few minutes I aspirate her runny nose)
Ambroxol HCl drops - 0.5mL oral drops, 2 times a day (for her cough)
Phenylpropanolamine (Disudrin drops) (nasal decosgestant) - 0.5mL oral drops, 3 times a day

I'm still observing my baby at the moment for any changes. My Aunt mentioned that maybe my baby is already teething early. Its just hard to see her gasping for breath due to her stuffy nose and coughing.

I just hope my baby will recover right away. For now, I just make sure that whenever by baby coughs she is either on her side or she is on an upright position.