Stressed by baby crying

My baby crying still stresses me out so much, I just feel like I can't cope as soon as she starts crying and I can't bear to let her cry for even 1 minute. There are occasions where there is nothing I can do about it, like when I'm driving (she hates the car), and I struggle to keep calm. Yesterday she screamed so badly she was sick, I was on a motorway I couldn't stop, I was literally crying with her. This has happened many times before. With her being mobile now she's also falling and bonking her head from time to time, and then she's hysterical and twice has thrown up through hysterics (not because she hit her). She also will not be cuddled when she's like this, pushes me away and just cries harder so I feel totally helpless. She's the same way in the night when she wakes crying. As soon as she starts crying I feel my stress level rising, I try so hard to remain calm but I fail every time and I know this won't be helping. I want to do anything to stop her but nothing will and she's so strong now and pushes away, arches her back, flings herself backwards, but if I let her go she cries harder. I have completely lost my cool several times, begging her to stop, shouting even (I know this is awful and I hate myself for it believe me), I've held her tightly to stop her throwing herself backwards and worried that maybe I've held her too tightly and hurt her, I just feel totally and utterly helpless in these moments. I feel like the worst mummy ever that I can't comfort her but also that I'm unable to just stay calm and get so frustrated, stressed and angry even. Is this a mental health thing? Do I need to get help? I would never ever hurt my baby but I worry that my reaction will be somehow emotionally damaging because I don't know how to be a calming presence for her and I don't know how I can learn to be calmer. Every single time I hate myself afterwards and promise that next time I will keep calm but I'm physically unable to. It's like I'm not in control of it at all.