Uller
Adventurer
DM's Guide: Swimming is DC10 once per hour to avoid a level of Exhaustion.
You're making regular swimming harder. It's your call to make, but I wouldn't do that bit.
This covers long distance travel and long periods of time in "unusual environments" and is a constitution save. It's got nothing to do with this particular subject.
The OP is talking about swim checks which are mentioned on page 175 of the PHB.