Is there any iPhone SE out there with 3D Touch?
You are correct, the iPhone SE does not have 3D Touch. What you most likely witnessed is that your cousin was running the iOS 13 Beta and as a result of this, Haptic Touch is now available on some older iPhones that never had 3D Touch.

In terms of what you can do about it, you’re in luck because iOS 13 is now available to the public. All you need to do is upgrade iOS and you’ll have the Haptic Touch support that iOS 13 offers (one that is almost identical to 3D Touch). 

That is, in iOS 13 Haptic Touch is now available in most of the ways that 3D Touch was available to 3D Touch devices (previously, in iOS 12 Haptic Touch was limited). However, the way to utilise it is by pressing on the screen continuously for a second or so, as opposed to applying more pressure in the way 3D Touch worked. Because this works on the basis of how long you're pressing, there's no need for special hardware, hence the reason why the iPhone SE can take advantage of this feature.

For more information, see the iOS 13 info on Apple's website.

To upgrade, simply go to Settings > General > Software Update.