I have been flying with our DS since he was 3.5 months old, several times a year, multiple legs each trip, internationally and domestic.
I agree with the PP statement about ears and pressure. I heard the same from FAs. We never experienced any problems with our DS.
I am a nervous flier and I completely understand your fear of panic attacks. If you are open to it, talk to your doctor about a mild anti-anxiety drug to take prior to flying. It made a world of difference for me. I went to feeling like I was going to lose my mind to actually being able to enjoy the trip. The stuff I take doesn't make feel weird or foggy, it makes me feel calm and capable which is how I need to be to care for DS.
Because of my anxiety, I have a need to leave nothing to chance. Here is what has worked (or not) for me when flying with DS -
I have never used a stroller for plane travel and never missed it. When DS got too big, I switched to a framed backpack carrier. I used an old duffle bag to gate check it. We (meaning the general public) can agrue the safety of gate checking baby gear until the cows come home but it worked for us. Worst case scenario, it would have needed to be replaced.
I learned to travel with the bare essentials. I take one change of clothing for each of us. I also swear by the ziplocs too. Each outfit gets packed in its own ziploc. Snacks go in another. Activities in another and so one.
One area where I don't skimp though is food and liquids. Don't count on either being available. I have seen parents begging for water or milk prior to beverage service as well as there not being enough free or purchase food to go around. I take enough food for DS to last him 12 hours.
Something I have seen recently is the gate agents/FAs not allowing carry-ons. Planes are flying at or close to capacity and passengers are bringing more and more on the plane to avoid baggage fees. Just something to keep in mind should you be forced to give up your carry-on. Also, they are closely checking the size of carry-ons. If it exceeds the airline standards, it gets gate checked.
Get to the airport early, early, early. Clearing security is so much easier if you aren't rushed.
We always take advantage of early boarding, when it is offered.
You asked about what to do if you need to use the restroom/holding the baby, don't count on any assistance from FA in terms any assistance.
Avoid the bulkhead. The seats are generally narrower as the tables are intergrated into the armrests. Also, you will lose the storage space that is available under the seat in front of you offered in regular seats.
It can't hurt to be asked to be seated next to an empty seat but as mentioned before, planes are so crowded now that empty seats don't seem to exist.
The Crew Lounge is a great resource for information. One of the hosts is a flight attendent and a mother. She gives awesome advice about flying with kids. The podcasts can be found at upgrd.com.