This is more than likely due to the beta-alanine. The pins and needles feeling you get on your skin after taking beta-alanine are referred to as paresthesia. It is a harmless side effect and is not an allergic reaction or an inflammatory response. It is caused by MAS-related and sensory neuron's response to the beta-alanine.
The theory is that beta-alanine activates G-protein-coupled receptors, which are responsible for transmitting signals throughout your central nervous system, and especially on the skin.
In other words, the amino acid fires up your nerve endings in a way that causes that beta-alanine to tingle and itch, but not enough to cause actual pain.
Beta-alanine acts at the cellular level to keep the pH within the muscle from getting too acidic, which contributes to fatigue. Therefore, beta-alanine delays neuromuscular fatigue, which gives performance benefits.
Note: If you are having trouble breathing, contact your nearest medical facility. This may be an indication of an allergic reaction to something else. Beta-Alanine is not known to cause an allergic reaction.