Yes, the astigmatism axis is very important for fitting eyeglasses to correct vision. From your description, i know you must suffered from astigmatism. And people who suffered from astigmatism usually difficult to focus somethings, and only the right prescription lenses can help them focus better. In fact, the astigmatism axis is as important as the SPH value for the prescription eyeglasses.
Yes, the astigmatism axis is very important to make prescription eyeglasses if you have astigmatism. If you provide incorrect astigmatism axis, you may get blurred vision or headaches even if the eyeglasses are made in exactly the right SPH, CYL and PD etc. So, You shall be careful.