K.T.
Have you tried letting her use the spoon? Even though she wont be able to feed herself very well, it could spark an interest. I know when my son was about that age he really wanted to hold the spoon and would spit his food out if I didn't give it to him. So I let him hold one and I fed him with another one. Eventually he would not let me feed him from a spoon at all and at that point I switched to only table foods.
My son also gags and chokes...actually he is almost 17 months old and still does maybe once every week or two. It scares me to death and I have tried cutting everything into extra tiny pieces but it still happens. He just does not take the time to chew everything thoroughly [he has all of his teeth including his 2 yr molars so there is no excuse]. I have had to tip him over and save him probably 60 times since he started solids. He has reflux and was a big puker as well - the big time, whole-stomach and/or projectile puking subsided by 10 or 11 months for us.
Anyway, my point is, even if you wait until she is older she may still throw up and choke. However it may help to just take a little break and try again in a couple of weeks. Then you can start again with a whole new attitude, and praise her on how she is "such a good eater" when she does eat well for you. I think she is probably ready to start trying some finger foods but you may want to coarse-grind or mash things first to introduce some texture and bigger bits. Also I would wait at least 2 hours after giving her a bottle to feed her to make sure she is hungry because it really does make a huge difference. Even if she is only getting bottles right now, she wont be on formula forever. It's not such a big deal in the long run. Just keep trying.