Personally, my kids didn't have ANY solids until 7 and 7.5 months old. They were exclusively breastfed, and didn't need them. Each chid is different and you have to see if your son is ready. However, most experts agree that waiting to introduce solids is best. The American Academy of Pediatrics suggests 6 months before introducing solids. For some reason, despite the fact that the AAP recommends waiting, pediatricians are so ready to suggest solids as soon as babies turn 4 months old. I don't agree with this.
The benefits to waiting on starting solids are many. You didn't mention if he's breastfed or bottle fed. Most of these reasons for delaying are for both FF and BF infants, but some (like greater protection from illness) are specific to exclusively BF babies.
Delaying solids gives baby greater protection from illness.
Delaying solids gives baby's digestive system time to mature.
If solids are started before a baby's system is ready to handle them, they are poorly digested and may cause unpleasant reactions (digestive upset, gas, constipation, etc.). Protein digestion is incomplete in infancy. Gastric acid and pepsin are secreted at birth and increase toward adult values over the following 3 to 4 months. The pancreatic enzyme amylase does not reach adequate levels for digestion of starches until around 6 months, and carbohydrate enzymes such as maltase, isomaltase, and sucrase do not reach adult levels until around 7 months. Young infants also have low levels of lipase and bile salts, so fat digestion does not reach adult levels until 6-9 months.
Delaying solids decreases the risk of food allergies.
Delaying solids helps to protect baby from iron-deficiency anemia.
The introduction of iron supplements and iron-fortified foods, particularly during the first six months, reduces the efficiency of baby's iron absorption.
Delaying solids helps to protect baby from future obesity.
The early introduction of solids is associated with increased body fat and weight in childhood. (for example, see Wilson 1998, von Kries 1999, Kalies 2005)
Delaying solids helps mom to maintain her milk supply (if BFing, obviously).
Delaying solids makes starting solids easier.
I know many people will tell you they started their kid at 4 or 5 months and their child was "ready," but I just wanted you to see the other side of the coin here. Also, the "your child will sleep better" is pretty much seen among experts as an old wives' tale. Formula is supposed to be close to breastmilk, so I see no reason why it has to be supplemented with baby food early. The oatmeal for reflux was prescribed for a reason. I don't believe that that means you have to give him baby food now. The pedi was giving you the green light, but as I said, that is NOT recommended by the American Academy of Pediatrics (ironic that pedis tell moms they can start when their academy says otherwise).