That is clear.
I get the same waveform on my scope without the spike that you are getting, so I think something has failed in your power supply.
If you feel like fixing it yourself, you obviously need to open the scope up.
Don't try and probe anything directly. If the ringing is on the primary, the amplitude of the ringing at over 100MHz will probably exceed your probe's ratings. What you want to do is to work out if the ringing is on the primary or the secondary. to do this,add some tape or something to a scope probe so it cannot make contact with anything and just use it as a proximity probe. In particular, you are looking at the switching transistor(s) on the primary, or the rectifiers on the secondary. The ringing should be much stronger on one side of the transformer to the other side.
From the waveform, it looks almost certain that the ringing happens when the switching transistor turns off. The other lower frequency oscillation at the end of the plateau is totally fine - that is standard in a flyback switching power supply where the core current is allowed to decay to zero.
If it turns out to be the primary, then as a start, it is not the switching transistors/mosfets or the transformer with the problem unless the transformer has an extra winding that is used only for a snubber diode circuit, and that winding has gone open circuit. See what other components are connected to the primary windings. If there is a snubber circuit, it could consist of resistors, capacitors or diodes.
Richard.