Hello, my name is***** and I have over 20 years of experience as a veterinarian. I am sorry to hear that Henry jumped head first into a bucket of paint.
I understand your concern as he may have ingested or aspirated some paint into his lungs.
Is he breathing normally?
Has he eaten anything since this occurred?
Was this water based latex paint?
The good thing about most paints manufactured now is that they are not very toxic. Accidental ingestion can lead to mild gastrointestinal upset if enough is eaten. You may see mild nausea, decreased or lack of an appetite, and/or diarrhea. But that should be it.
I would rinse his mouth out with cool water. Then you can offer 1/4 cup of milk to drink to coat his gastrointestinal tract to try to ease any irritation. I don't normally recommend giving milk to cats as they are lactose intolerant in most cases, but I think it is worth it in this case.
If his appetite seems off you can offer a bland diet of 2/3 boiled, skinless, white meat chicken minced mixed with 1/3 boiled, plain white rice. This is an easily digested bland diet and won't irritate his stomach and intestines. Feed the bland diet mix for several days until his nausea clears, then slowly start mixing in his regular diet. It should take about a week to convert him back, mixing a little more regular and less bland in each meal.
If he seems to be breathing differently, (faster than usual, labored breathing where he seems to struggle to breathe) is coughing or his gum color is blue/gray in color then he should see a veterinarian for an examination.
Please let me know if you have any further questions.