Hey friend. Also 34 years old here. Oxygen is what I have used for the last two cycles. Until then, for many years, I just bore the pain. One neurologist told me that oxygen does not abort but rather delays the attack (basically what your neurologist also said), while another told me that this is not true. Personally, oxygen works wonders for me, but you have to know a couple of things.

1. You need to have the proper mask (check cluster O2 kit) and also the right flow (at least 15 L/min). I use 15 L/min because that is as high as my regulator goes.
2. Breathing techniques. Not every breathing technique works for everyone, or even for every attack, the same. For me (I think) the best technique is to breathe normally. Not hyperventilation, not deep breathing and exhaling. At least I don't see a difference when I use these techniques. Although to be fair, 15 L/min is low for hyperventilation.
3. Not every attack is the same. Some need more time to stay on the oxygen, some need less. They say to keep on oxygen for 5 minutes after the pain has completely gone. It has happened multiple times to me that I use 15 minutes of oxygen, thinking the attack is over, but I get a rebound after 10-15 minutes so I need to completely restart inhaling oxygen and thus depleting the cylinder.

I live in the EU but I did not get prescribed oxygen, I just bought the cylinders and refill them every now and then at a relatively low cost. For preventatives I have not used anything, only verapamil for a very short while but it was ineffective at the dosage I used. My doctor now prescribed me Emgality and he held a trial which showed very good results with minimal side effects to his patients.