Attention Deficit Hyperactivity Disorder (ADHD): This condition is characterized by symptoms of inattention, hyperactivity, and impulsivity, which can also include irritability and emotional deregulation. The age of the child and the combination of symptoms make ADHD a strong consideration.
Oppositional Defiant Disorder (ODD): Often co-occurs with ADHD, ODD is marked by a pattern of angry/irritable mood or argumentative/defiant behavior. The symptoms of irritability and outbursts align closely with this diagnosis.

Anxiety Disorder: Anxiety can manifest as irritability in children, and given the mention of anxiety, it's plausible that an anxiety disorder (such as generalized anxiety disorder, separation anxiety disorder, or social anxiety disorder) could be a primary or contributing diagnosis.
Mood Disorder (e.g., Depression or Bipolar Disorder): Though less common in young children, mood disorders can present with irritability and emotional deregulation. Bipolar disorder, in particular, is known for mood swings and could be considered, especially if there are episodes of mania or hypomania.
Disruptive Mood Dysregulation Disorder (DMDD): Characterized by severe recurrent temper outbursts and persistent irritability, DMDD is a diagnosis to consider in children who exhibit these behaviors.

Traumatic Brain Injury or Other Neurological Conditions: Certain neurological conditions can cause changes in behavior, including irritability and outbursts. It's crucial to rule out any underlying neurological issues.
Thyroid Disorders: Both hyperthyroidism and hypothyroidism can cause mood changes, including irritability and anxiety.
Sleep Disorders: Sleep disturbances can significantly affect mood and behavior, leading to irritability and outbursts.
Substance Exposure: Though less likely in a 6-year-old, exposure to substances (either through maternal use during pregnancy or direct exposure) can lead to behavioral changes.

Pervasive Developmental Disorders (e.g., Autism Spectrum Disorder): While not typically presenting solely with irritability and anxiety, children on the autism spectrum can exhibit these symptoms as part of their disorder, especially if they have co-occurring conditions.
Genetic Disorders (e.g., Fragile X Syndrome): Certain genetic conditions can lead to behavioral issues, including irritability and mood swings.
Infectious or Autoimmune Encephalitis: Though very rare, conditions that cause inflammation of the brain can lead to sudden changes in behavior, including irritability and anxiety.

Treatment will depend on the diagnosis but may include:

Psychotherapy: Cognitive-behavioral therapy (CBT), family therapy, or other forms of talk therapy can be effective for many of these conditions.
Medications: Depending on the diagnosis, medications such as stimulants for ADHD, mood stabilizers for bipolar disorder, or selective serotonin reuptake inhibitors (SSRIs) for anxiety or depression might be prescribed.
Lifestyle Changes: Improving sleep habits, increasing physical activity, and reducing stress can also be beneficial.
Educational Support: For conditions like ADHD or autism spectrum disorder, accommodations in the educational setting may be necessary.