As you are in the severe/profound range, It is possible to get referal from your ENT (i don't know where excatly you live) I am from UK (south) and when my HA doesn't seem to be loud enough, I got Referal from my ENT to CI Centre where they would give an Intial assessment, it's an assessment to see if a person are eglible to go on to full CI assessment, it's simple, just few hearing tests, the speech discrimation tests.
Be prepared for long wait, I was lucky i had my CI 10 months after referal, the norm is 2 years waiting depending on where you live. You will need to make appt with your ENT first then go from there.
CI is paid for By PCT but again that depends on your local PCT.
I don't see the harm in trying out. Good luck
Haven't heard bird sing yet as i was implanted in July and the birds aren't singing until spring! But I do hear alot more than i ever did with HA's. I can hear computer tapping, and clicking as i change the page on the website!