In order to answer this question, it is helpful to think about what causes acne
in the first place. Basically, acne occurs when pores of the skin become clogged with dead skin and other debris. This allows bacteria to collect and build up and can lead to inflammation and pus ("whiteheads"). All of the various treatments for acne that work involve trying to remove this layer of dead skin and debris, or reducing the bacterial activity on the skin.
Therefore, there is no reason why touching your face with your hand per se would cause your face to break out. However, if your hands are dirty or oily, you may be transferring this debris to your face, which could potentially cause a problem. Similarly many people when they touch their face, what they are actually doing is picking and squeezing at areas of acne. This definitely will worsen the situation, as it causes inflammation and can lead to infection or scarring.
The best way to treat your acne is, therefore, to avoid squeezing the affected areas of skin. Follow this up with daily face washing, exfoliation, and, if necessary one of several acne products containing benzoyl peroxide or salicylic acid. If this does not work, then you should consult with your primary care doctor
or your dermatologist