While it is occasionally possible to be allergic to certain components of makeup, the skin reaction you are describing doesn't sound like an allergic reaction. Rather, it sounds like acne
Acne commonly is associate with wearing make up. This is because acne occurs when the pores in the skin become clogged by debris. Make up is one of the primary pore-clogging culprits!
In order to help cut down on the amount of pimples you get from wearing acne, it is very important to have a good facial cleansing regimen every night. You will want to start, after completely removing your makeup with tissue, with a good facial cleansing soap and a gentle exfoliating regimen.
If this doesn't work, you will want to consider adding a comedonolytic. Comedonolytics are chemicals that help to strip debris out of clogged pores. The two most common comedonolytics are benzoyl peroxide and salicyclic acid. Both of these are found in many common over the counter acne preparation, and you should be able to find one just by reading labels in your local pharmacy or supermarket.
If this doesn't work, you will need to consider cutting down on the amount of makeup you are wearing.
I recommend talking with your primary care doctor
for more information.