Your question about personality types and the importance of expressing feelings and emotions is one that numerous authors have spent entire books trying to answer. While this is a huge subject, we will try to distill some of the concepts involved with biblical principles for you to consider.
From your use of the term "phlegmatic," it seems that you already understand that people have different personalities or temperaments. One of the older methods of classification describes people as being sanguine, choleric, phlegmatic or melancholy.
In recent years, there have been many newer classification models offered by various individuals, almost all of them based on four descriptions of personality types. One of the most obvious areas of personality identification considers whether a person is generally quiet in contrast to being more expressive. In the Myers-Briggs personality type indicator system, the one most heavily researched and used in the United States, this contrast is referred to as being an extrovert or an introvert.
According to Myers-Briggs data representing hundreds of thousands of people, the U.S. population reflects about 2/3 extroverts to 1/3 introverts. That is one reason the U.S. culture values extroversion (expressing oneself) over introversion (keeping one's thoughts inside). Other cultures, such as those in Asia, value introversion and find extroverted Americans to be overly demonstrative and too talkative. Theoretically, as we mature, we become more comfortable going beyond our preferences (acting more extroverted even if we are introverted, for example). Yet in times of stress, we all tend to revert to our innate preferences.
While there are three other areas of personality identification, let's now focus on your specific question regarding extroversion/introversion—whether as a Christian you should express yourself or remain quiet. The Bible has much to say about communication, because according to our words, we will either be justified or condemned (Matthew 12:37). The reason for this basis of judgment is that we all tend to speak what we think (Matthew 12:34; Luke 6:45). What we are thinking is, thus, the real issue.
Being an extrovert can be either good or bad depending upon what we are thinking. Proverbs 10:19 (NIV) says, "When words are many, sin is not absent, but he who holds his tongue is wise." Ecclesiastes 5:3-7 says "many words are meaningless" when there is a wrong orientation. Christ likewise said, "And when you pray, do not keep on babbling like pagans, for they think they will be heard because of their many words" (Matthew 6:7, NIV).
In contrast to these scriptures, expressing "many words" of God's truth is good (Acts 2:40; 15:32). Likewise, we are told to encourage each other with God's truth (1 Thessalonians 4:18; 5:11). Hebrews 3:13 speaks of encouraging "one another daily." Peter tells us to be ready to give an answer to anyone who asks us about God's truth (1 Peter 3:15).
In considering these passages, the lesson for us is that personality type is never an excuse to sin, nor is one personality type better than another. God expects all of us to act like Christians regardless of our temperament. If we are extroverts, we would do well to make sure what we are saying is godly. If we are introverts, we need to make sure that we don't neglect encouraging others through our words.
As for how much of our personal feelings and emotions we share with others, each of us makes this decision based upon our personality type and our relation to the individual involved. If the person is our parent, the Fifth Commandment tells us to honor our parents and, thus, we should strive to share our feelings with them. Likewise, husbands, out of love for their wives, should share their feelings with them to build trust. We may also choose to self-disclose our innermost thoughts to a close friend. On the other hand, we are not obligated as Christians to share our innermost thoughts and feelings with strangers or simply anyone who asks.