One of two things is happening: your skin is either purging or you are having a reaction/adjusting to a new skincare product.
Purging is the skin's way of eliminating excess sebum or impurities underneath the skin, generally through the initial process of breaking out. It sometimes occurs when using an acne-related product (cleansers, exfoliants, and other topical medications such as salicylic acid, retin-a/tretinoin, and benzoyl peroxide). Some pore blockages come out easily, while others do not, which then causes a whitehead or an inflammatory pimple.
Reactions to new products can also cause initial breakouts (along with irritation and other symptoms). Some people may be more sensitive than others, especially when using topical medications that exfoliate the top layer of damaged skin. The thinner the top layer, the more prone you may be sensitivity or allergic reactions. Unlike purging, new product reactions can occur with a full range of skincare and facial makeup products. Over time these reactions should subside.
How long the initial breakout may last differs from person to person. It depends on how sensitive your skin is, and also the extent of your acne was before you started the new product. For example, a person who had a face full of clogged pores may experience a more severe initial breakout than a person only suffering from a blackhead on the side of his/her nose.
The best advice is to stick with it. Any legitimate skincare treatment will take time and consistency to work. Taking care of your skin is a long term commitment.