A.,
Congrats an your little one! I would suggest taking her to the Dr. and asking them to educate you about trace aspiration that can cause cold or respiratory type symptoms. Sometimes you can try "Thick-It" to thicken the formula or breast milk just enough to slow dowm the flow of the breast milk or formula allowing her more time to coordinate the suck/swallow responce. They may have other recomendations for you to try, or may refer you to a feeding therapist {usually an occupational or speech therapist}.
A very important part of this equation is to avoid causing an eversion to feeding or oral stimulation. Some of the ways you con do this is by providing a lot of positive experience around the oral area. For example: lots of playful {always Pleasant} touch around her mouth, Making sure she has Teething type toys that she will playfully {soon on her own} bump into her face, tapping your fingers on her lips as she makes noises... All should be very pleasant interactions between the two of you! Start outside of the mouth then progress to the tip of the tounge and further into the mouth as she will allow. Deep pressure is usually tolerated better than light touch. IN other words, she should know exactly where something is around or in her mouth rather than feeling like it could possibly be going to choke her. Of course, don't put anything in there small enough to choke her. A pacifer may be a good thing for her to begin to experience her mouth as an area of comfort sa well as soothing. this way she is more likely to accept the nipple for feeding. All of these things should be done very slowly{over weeks} and ALWAYS a pleasant experience for both of you.
Sometimes feeding problems can become longterm if everthing around feeding becomes a negative experienc. So....keep it pleasant and get help if things keepbeing scary for her.
Best of luck!
P.S.
Aspiration can happen in very small amounts. If they do test for it, {probably after trying things clinically} they would do an oral-pharngeal motility type study by a radioligest. They would first probably have here swallow barium {hopefully the same thickness of her formula} and if they see aspiration May want to try giving her a few swallows that has been thickened with a thickening agent intended for infant foods to see if the thicker consistency stops the aspiration.
Also, When feeding, try to keep her positioned in as upright position as possible and keep her from tipping her head way back while feeding.