Being frightened of the next one is common, and it has a name
Roughly one woman in six meets criteria for severe fear of childbirth, and the strongest predictor in a woman who has given birth before is a previous bad birth.
If the thought of doing it again makes you feel sick, you are not unusual and you are not being dramatic. This is a measured, named thing.
Pooling 29 studies and 853,988 pregnant women, about 14% met criteria for intense fear of childbirth. The largest and most recent analysis, 67 studies and 905,504 women, found severe fear of childbirth in 16.5%, roughly one woman in six. Its authors summarised it as affecting about one in six women globally.
Take those figures as an order of magnitude, not a precise rate. Studies ranged from under 4% to over 58%, mostly because they used different questionnaires and different thresholds. Even when researchers looked only at studies using the identical tool and the identical cut-off, national rates ran from 6.3% to 14.8%. Somewhere between one woman in sixteen and one in seven is the honest range.
The part that matters most to you is this. In women who have given birth before, the strongest predictor of fear is a previous negative birth experience or an operative birth. Researchers in this field argue that fear of childbirth and fear after a birth should be counted as two different things, because the second one has a cause. Yours may have a cause, and it is not cowardice.
There is treatment, and the evidence for it is mixed in an interesting way. A Cochrane review of seven trials of non-drug support, including counselling, psychological therapy and group work, found that the reduction in measured fear may not be large enough to be meaningful. But in the same trials, fewer women in the support groups had a cesarean, and fewer wanted one, on moderate-certainty evidence. The underlying rates in each group were not available for this guide, so no plain per-hundred figure can be given here for either of those. All seven trials were unblinded, which weakens them.
"Is there a service here for fear of childbirth, and can I be referred now rather than at 36 weeks?"