Yes, this is quite common. Many women find that they get more sensitive to things during the menopause. You could look at organic skin care ranges, as most general make up products do contain lots of chemicals and this may be part of the problem. A cup or two of nettle tea a day can often help minor allergy-type reactions, and boosting your immune system with herbs such as Echinacea may help as well. Make sure, too, that you are eating plenty of vitamin C rich foods, as vitamin C is excellent for the skin and also reduces the severity of allergic reactions.
Comfrey is a herb which is known to strengthen tissue, it's old fashioned name was Knitbone as it was used to help repair bone fractures. Nowadays we recommend Comfrey Cream for tired, weak skin that needs a boost and it can be used both as a day and a night cream. I find it particularly good as a hand and nail cream and I use it here as well every night before bed.