Try to wear a high-collar base layer underneath to avoid contact between the coat and your neck. Wear a scarf, or if you are a woman, a silk scarf, which can protect your neck from being pinched. Due to the material of the woolen coat, it may cause pricking. You can try soaking the woolen coat in softener and then clean it.

You can sew the back collar of the dress inward, make small modifications, and then sew an icon on the seam that you think will not make the dress look weird. This depends on the person. If you want to make major changes, put a collar on it.