Well, some babies who have acid reflux don't actually spit up; this is the silent form; it only comes up part-way.
Congestion IS very common among newborns and very young babies. BUT if you are feeding her dairy-based formula, it could be that. Dairy causes congestion, and some people are more sensitive to it than others. Try switching to a soy-based formula. Make it organic if you can, because most soy in the United States is genetically modified. (It's even worse in the case of dairy, because the cows are being fed genetically modified soy and corn - another crop that is genetically modified nearly across the board now - and the genetically modified proteins bio-accumulate and can pass through the milk; this, and dairy cows are injected with genetically modified bovine growth hormone to increase milk production. All of these things are profit-driven without a lot of concern for people's health. They do bare-bones safety studies of extremely questionable quality to get their product on the market. In short, go with good, old-fashioned straight-up organic when possible, especially when it comes to soy, dairy, and corn. I could tell you about other crops you want to buy organic, but that's another subject. PM me if you're interested.)
Anyway. Try a can of soy and see if her congestion clears up within about a week (it can take a few days to a week to see the difference). I bet you it will!
The severe congestion around Christmas was probably a result of the new addition to her diet. The cereal, while still very wet, is drier than formula or breast milk. What I learned from Ruth Yaron's Super Baby Food (a fantastic book, please get it!) was, when you feed a baby a meal of solids, you need to offer the baby a little water, too. This is also important not only to keep them from getting congested, but also on the other end, to prevent constipation.
Of course, she might also have had a bit of a cold.
Hiccups - lots of them - are very common among babies. Lots as in, oh, a couple to several times a day. Hiccups are not a symptom of reflux.
I'm surprised that the doctor approved feeding solids so early. All the studies show that even four months of age is still early to be starting a baby on solids. Most doctors that I've talked to - and my mother, a nutritionist who sees young babies at WIC - have told me that closer to six months is safer. You might want to put it on hold for at least another month to help prevent food allergies in her. If it can be prevented by just waiting a month, by all means, wait a month!! For her sake, and yours. Food allergies are a pain in the neck in the best case, and fatal in the worst.
Here's why it causes food allergies: at this age, anything other than breastmilk or formula is hard for their digestive system to deal with, and this stress on the digestive system can lead to a strong reaction to certain proteins - this reaction is a food allergy. How my pediatrician put it was, there's no harm in waiting another month, but there could be harm in starting solids early.
Does this doctor say that the cereal will help with the reflux? Because it is "heavy" and will sit in the stomach better without coming up? If so, this is completely wrong.
Send me a private message about any other issue that might be motivating you to use cereal at this time. (Are you trying to get her to sleep through the night? That's another old wives' tale! It doesn't work and might actually make night waking worse.) Maybe I can suggest an alternative to feeding her cereal that will resolve whatever problem it is that is making you want to use cereal. You have options!
To tell it to you straight, the advice you're getting doesn't sound very good. Maybe you should find a different doctor for your baby. It seems pretty common, from my experience so far, that doctors still hold onto a lot of outdated "wisdom" that has been proven to be old wives' tales, and they just haven't caught up with newer research. It's like they are going with what they learned way back in med school. Hair stylists need to take classes every few years or so to catch up with new hair styles. You would think doctors would have to take classes to keep up with research for the sake of our health! But, anyway, it sounds like you and your baby are on the short end of this situation. Set up appointments with other doctors in different pediatric practices/offices and see if you click better with someone else. These interview visits should be free for you, but sometimes aren't.
Good luck! Hope to hear from you!
L.