Each of us has significant variations in how we experience emotions. In some people, such as you describe yourself, emotions are very present, perhaps too much so and can cause embarrassment and difficulties.
You can blame your genetics for much of this. Although our development plays a part of the problem, our biochemistry contributes a great deal to the problem. This is most likely why you have not done as well with self help and counseling.
Let's look at some best practices for this problem:
The type of therapist that you see will make a big difference in how well you do with this problem. Some therapy viewpoints will actually make you more emotional in the short run, not less. However, CBT or cognitive behavioral therapy is an excellent resource for dealing with emotional stability. The therapy looks at your thought process and helps you change your thoughts, which in the majority of cases influences your emotions.
Many women discover that a physical cause has influenced their emotions for many years; in most cases they were unaware of the issue. Thyroid issues, estrogen levels, blood sugar levels and even levels of neurotransmitters such as serotonin can play a big part of how you feel.
It is best practice to rule out these types of physical problems. One of my clients had problems similar to your own and was amazed at what a low dose of antidepressant did for her. As a good rule of practice, you may also want to look at a low dose of mood stabilizing medications as this can help stabilize moods that otherwise are difficult to control. These medications are well researched and can help tremendously with biochemical related problems. Please do not be discouraged at this as our bodies biochemically can cause many issues, including mood based ones. This is not your fault; it is simply the way your are made.
Diet also plays a critical but often overlooked part of this as well. Diets rich in nuts, bananas, an whole grains can greatly influence serotonin and mood stability. 1000mg of Omega 3 has been show in legitimate research to stabilize mood and assist in neural health. On the other hand, red meat consumption has been shown to have a negative relationship with mood stability in some individuals.
Based on what you are saying I would try a two tiered approach:
1) See your family doctor to rule out any unknown physical contributers to the problem. With you physician's guidance a change in diet will also be helpful and certainly has been shown to help some people with mood stability.
2) Seek out a CBT oriented therapist. Even if you saw one before, the skills and abilities within the field vary considerably and another therapist is worth a try.