Hi, I'd like to help you with your problem.
From what you are saying, it sounds like you had a close relationship with your dad and that his death has affected your life, including your relationship with your girlfriend.
From the symptoms you described it does sound like you are depressed. The typical symptoms of depression are: crying, decreased interest in pleasurable activities, weight changes (either loss or gain), sleep disturbances, fatigue and general feelings of helplessness or hopelessness. You may have all or just some of these symptoms. Your dad's death may have triggered the depression or made your problem with depression worse.
You mentioned that your girlfriend suggested counseling. I'm going to do the same and suggest you seek out a counselor to talk with. Depression can be helped greatly by therapy. You may also consider medication if you feel that you are having trouble functioning with everyday tasks and responsibilities.
Depression is easily treatable. With help, you can go back to feeling yourself and reconnecting with others.
I wish you the best.
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