A. Because he is having difficulty breathing and is so young, a visit to your Pediatrician would be a good idea.
One common thing that could cause symptoms like this is gastroesophageal reflux.
And that would mean that he is simply spitting up the breastmilk or formula that he is drinking. This is especially likely if it is happening more often right after his feedings.
When infants spit up, it is not uncommon for it to come out of their nose, so this may be the 'thick mucus like stuff' that you are seeing. And many infants arch their back when they spit up and some do choke or having trouble breathing.
Unlike the typical 'happy spitter' baby, who has reflux, but is feeding well, is gaining weight, and is not fussy, choking or having trouble breathing, if your child is frequently choking, then he might require treatment with an acid reducer. If your Pediatrician agrees that it is reflux, some of the typical 'lifestyle changes' for treating reflux might also help. See our guide to reflux for more information.
