I would nurse him all day as much as he wants and forget about table food. He will be able to digest that much quicker and it will keep him hydrated. Give little sips of water if he'll take it, or plain electrolyte water or coconut water (NOT Gatorade or something with sugar/colors.)
Call your ped- I would not take him in unless it continues or you are really worried about breathing. There is wheezing, which is a sound on the EXhale and there is stridor, which is a sound on the INhale. Wheezing they don't usually worry about, but stridor is a sign of croup. Putting him in the bathroom with a hot shower running in the background to create steam will help open him up, and cold air can help too, so standing by a window or bundling him up and taking him out for a breath of air. Croup swells the airways, so if you see his chest caving in when he tries to inhale, you should go to the ER for a breathing treatment right away (they will do a quick chest Xray most times too, to rule out pneumonia.)
The ped can prescribe a nebulizer you can use at home with asthma meds to temporarily help open up his airways or you can use sterile saline more frequently. The way I used mine at this age was to just aim it at baby's nose while nursing and comfortable. Even if they cry, they still get the meds during those deep breaths and it's good to help open them up.
It doesn't sound like a tummy issue to me, but a breathing one, and like the phlegm is congesting him and possibly upsetting tummy.
Kudos to you for co-sleeping and continuing to breastfeed him!! You are doing all the right things to keep him safe, healthy and comfy, especially while sick!
(mommy of a 3 yr old still nursing!)