Is It Normal to Get Facial Sores After a Chemical Peel?

Chemical peels are an important part of cosmetic medicine and can induce very specific and positive changes in the skin. Recovery after a chemical peel depends primarily on the depth of the peel.
Its not uncommon for chemical peels to reach the depth of the papillary dermis, causing epithelial slough after the peel. This skin exposure is not uncommon and will reepithelialize quickly if protected. In some cases, the peel can be patchy and reach unequal depths and cause problems.
The important part of chemical peel recovery is to recognize the difference between a normal peel depth and healing or infection. This postprocedural period is important and close follow up is crucial to prevent worsening of the condition.

Facial sores can happen with any peel of laser treatment that removes the outer layers of the skin. I usually have my patients take an oral antibiotic and an anti-viral medication until the skin heals.

Ulcers can mean many different things. As noted, this could represent an infection or a herpes zoster outbreak - both of which need immediate treatment. In general, regardless of the depth of a chemical peel, ulcers should not be a permanent result of the procedure. The best thing to do is to visit your doctor.

A properly performed chemical peel should not result in facial sores or open ulcers. A herpetic infection is a possibility but this would initially appear as a cluster of small blisters. For most deeper chemcial peels patients are treated with an antiviral agent to help prevent this complication. If a chemical peels goes down too deep in an area is can result in a deep skin injury. There are many variables involved including how your skin was initially prepared, what type of peel was done and what agents were used. You should report this finding to your physician as soon as possible to prevent any possible scarring.

I'm not exactly sure what you mean by sores. You should contact your physician as soon as possible though.
Chemical peels and laser resurfacing can cause a herpes flare up. (~50% of teenagers have been exposed to HSV-1 and 80% of adults have been exposed to HSV-1).
The herpes virus lies latent or dormant in our nerve endings. More often than not it does not spread and does not flare up. So, even if you've never had a herpes flare, you may still have been exposed to the virus.
Peels injure the skin and can lead to a flare up, i.e. a herpes outbreak. This is something that can be treated medically, but should be done so quickly.