With most jet skis, when they are towed you need to use a tool to pinch the feed hose or water will enter the engine while being towed.
I am sure this is what happened to you.
And yes, I would change the oil.
Here is a cut and paste on towing...
What you should know BEFORE you tow
If you need to tow your Jetski back to shore or to the marina you
have to clamp off the hose that supplies cooling water or you can fill your engine with water.
Check your owners manual for the correct towing procedure for your ski.
It cannot be emphasized enough that towing is extremely dangerous. Contact Elephant Butte State Park Rangers @ 575-744-5421 if you need to tow.
Make the fact that you are towing highly visible to other boaters. If the towing boat does not have any signal devices(!), waving
a brightly colored flotation device can help alert other boaters.
If you stop by the shop on the way to the lake Captain Pete will mark the appropriate hose to clamp off at no charge
This way you'll be prepared in the event you need to tow your ski
Since a Jetski that requires towing likely requires service, contact Captain Pete as soon as possible when there is a towing event.
If your ski sinks or fills with water, have it serviced as soon as possible.
If the engine isn't cleared of water and run within a day or two, there is a good chance it's life will be over or severely shortened
Attempting to restart a drowned engine can result in <pictures of carnage here> bending connecting rods and destroying the engine.
Check your owners manual for the proper direction to turn your ski in the event you flip it over.
Turning it the wrong way increases the chances your engine will end up ingesting a large amount of water.