9V 1A adapter and 2*3.7V battery IRF9630 produce sound and gets very hot 9V battery not (metal detector)?
Place a 1 ohm resister in the source of your P channel drive fet Q2 .Measure the voltage across the resister     with a scope  .If you see  big spikes like several volts then excess current is heating the Fet.  More Inductance  ,less on time ,More delay time will cool things down .Next place the scope between the Drain and ground noting a positive swing of almost 9V and a big negative backswing .If thin negative going backswing exceeds the VDs rating of your 200V P channel fet the Fet will zener and heat up because the inductive energy is going into the avalanche region of the Fet . Reduce on time ,Increase L1 ,Decrease R2 .High voltage P channel devices are hard to find .Next check the gate drive waveform on the scope expecting a clean square wave .Long fall times and parasitics will cook the Fet .