At 4 yrs old I didn't have any problems teaching our son how to use a neti pot.
I got it ready and supervised.
He didn't always like it but he always felt better for a time after using it.
Rinsing out the nose to help clear out mucus - and the saline solution helps to soothe where the mucus is coming from so it seems to help it slow and eventually stop the running nose.
If your son can gargle salt water and spit it out (and not swallow it) - then that will help his throat.
Keep his fluids up - soup broth, and tea with honey feel pretty good on a sore throat.
Sometimes snacking on a salty snack might help for a short while - like pretzels.
He doesn't have to do cough drops - just sucking on any hard candy can help - so try him on butterscotch drops or any hard candy that he likes.
When our sons tonsils swelled up - he didn't have a fever so they were not infected - they swelled up so much they were almost an obstruction.
Shrinking them with steroids was temporary and didn't work.
So we had his tonsils and adenoids out right after his 4th birthday and it was the best thing we ever did.
Being able to breathe, swallow, eat and sleep without snoring was great for him and his rate of catching colds went way down to only once or twice per year.
I hope your son feels better soon.
Additional:
Vicks on the chest and throat works for me.
When I'm sick I like the smell of it.
I tried the putting it on the feet thing and for me it doesn't work but it's worth seeing if it will work for your son.