tracheostomy- to do or not to do

a case report, 18 years old girl
ASA 2 premorbidly
ventilated for 2 weeks, for severe drug poisoning
that drug does not have anti-dote
with inotropic support near maximum
and maximal ventilatory support
endotracheal tube in place, which makes her lips eroded and ulcerated
her vital signs parameters were near normal only
so what to do next?

here tracheostomy whether mandatory?
p/s she has a short neck and is kinda obese..
if yes, who should do it? anaesth? surgical? ENT?
where should it be done? ICU? OT?
what method should be used? percutaneous? open method?

medical should not have heroic thing to be done
and that has been done should be beneficial to patient...

finally a tracheostomy was done, but patient deteriorating..