From what you say, you just doubt she must have swallowed the splashed water with oil.
Did she cough/ vomit after that?
Usually when kids aspirate, they have a bad cough with or without problems in breathing.
And small quantities when ingested... as with splash will not be a problem.
But if you are not sure of the amount of oil ingested , its better to visit the ER, have her examined by a doctor.
Fussiness may be due to some other reasons like a viral illness, tummy problems, ear ache
or a simple nappy rash
. A visit to your doctor will help you.
Hope my answer helps you.
Wish a speedy recovery for your kid.