Try "Shortcuts" it's an App (I believe owned by Apple now) that used to be called "Workflow." You'll for sure be able to set up an alarm called "My Second Time

Try "Shortcuts" it's an App (I believe owned by Apple now) that used to be called "Workflow." You'll for sure be able to set up an alarm called "My Second Timer" and set it to ask Siri to toggle the alarm on/off and use a variable for the number of minutes. Then you can use the "scripting" module to calculate current time + however many minutes to set the time to set the alarm when you trigger the event. Not ideal to need a workaround like that but at least you can run two "timers" without clogging up your alarm settings.