Whenever I hear symptoms like yours, the first thing I suggest is a visit to your medical doctor. There are many physical problems that can cause anxiety and mood changes — especially at your age. If you are still seeing a pediatrician, you might want to request a referral to an endocrinologist. It’s important not to jump to the conclusion that the problem is mental before checking out the physical. If you do have a medical problem and it isn’t attended to, it could get worse.
If are physically fine, then it would be helpful for you to see a therapist. It may be that you do have anxiety or you may be depressed. Depression doesn’t always show up as sadness. It can also show up as anger and feelings of emptiness. You also may have some unresolved issues regarding your father’s alcoholism and absence.
A therapist will be able to assess the difficulty and will make recommendations for how to treat it. Since your mother is doing her best to be supportive, it would be helpful if you included her in the appointment. With some coaching, she may be able to provide you with more helpful support.
I remind you that going for an assessment doesn’t obligate you to getting into therapy. You may or may not want to proceed. But the assessment alone may give you and your mom some new perspectives on your distressing feelings and what can be done about them.
I wish you well.