Welcome to FT, Maya!
We have found that a good doggy carrier makes life a lot easier for us and our dog. We use a
Jet Set carrier which has openings on both sides; can be used as a shoulder bag, tote bag, or backpack; and mesh on the sides to keep it relatively cool (but which can be covered if you want added discretion as you go around the terminal). You can also use it as a car restraint device with a seat belt and keeping one of the ends opeen. When we got it, we got our dog used to it over several days, increasing the amount of time he spent in it (sometimes carrying him around the house as we cleaned or did laundry to have unexpected movements; sometimes leaving him by our feet) and always praising him when he came out. He absolutely loves his carrier now and begs to go in it as he knows that fun is coming!
I suggest you get a carrier you like and get your Chihuahua used to it ahead of the flight so it's not new/scary and your Chihuahua knows to expect fun when you (finally) land in SFO.