Go through these in order and stop at the first one that applies. If you are reading this for someone else, answer for them.
Call emergency services now if someone exposed to oil-based paint:
And for anyone, someone who:
Contact a poison control service promptly after any oil-based paint ingestion, even if there are no symptoms.
In the United States, Poison Control can be reached at 1-800-222-1222 .
Elsewhere, use your local poison information service.
Have the container or product name available if possible.
Urgent medical assessment is also appropriate for persistent coughing, choking, vomiting, increasing drowsiness, breathing changes, or ongoing eye pain after rinsing.
And for anyone, someone who:
Arrange routine follow-up for symptoms that continue after the initial exposure, such as cough, reduced exercise tolerance, numbness, balance problems, or difficulty concentrating.
Repeated workplace or hobby exposure should also be discussed during routine care, ideally with the product's safety data sheet.
The article also says
Do not enter an enclosed area filled with paint fumes to attempt a rescue unless it is safe and you have suitable equipment.
Every sign above is quoted from the sofidex article on Oil-based paint poisoning. If you are not sure, err upward — it is always reasonable to be checked.