The COVID-19 pandemic is having negative consequences not only for people’s general health but also for the masticatory system. This article aimed to assess confinement and its new normal impact on well-being, sleep, headaches, and temporomandibular disorders (TMD). An anonymous survey was distributed to a Spanish university community. Participants completed a well-being index (WHO-5), a questionnaire related to sleep quality (the BEARS test), a headache diagnostic test (the tension type headache (TTH) and migraine diagnosis test), and the DC-TMD questionnaire. Questions were addressed in three scenarios: before confinement, during confinement, and the new normal. A total of 436 responses were collected (70% women, 30% men). A reduction in well-being and sleep quality was recorded. Respondents reported more TTH and migraines during and after confinement. Overall, confinement and return to normal did not increase TMD symptoms, and only minor effects were observed, such as more intense joint pain and a higher incidence of muscle pain in women during confinement. Reduced well-being is correlated with sleep quality loss, headaches, and TMD symptoms. This study provides evidence that pandemics and confinement might have had a negative impact on population health. Well-being was strongly affected, as were sleep quality, depression risk, TTH, and migraine frequency. In contrast, the temporomandibular joint and muscles showed more resilience and were only slightly affected.