Re: flying with a 3mo old?
Take your car seat. The ones they rent may not be good or safe. And, yuck as they probably never clean them.
Bring your seat and gate check it. Ask for an extra seat if they have them available. You can hold baby but its nice to have that seat just in case. We did a lap baby at 11 months and honestly it scared me and I would never do it again. He slept most of the way but still. On the way home they gave us a free seat and it was far more secure. I'd bring a snap and go for an infant seat. We brought our corroco and strapped it into our jogger - it fit great. Buy a bag for the car seat. You can get one made for car seats or get a large duffle bag.
Rent one of the luggage carts at the luggage area. They work very well.
Mom to my wonderfully sweet toddler who is the joy of our lives.