Swimming - suggests you feel as though you are swimming through the depths of your subconscious and emotions. The ease with which you are doing this activity will give you clues as to how well you are navigating through those very complex parts of yourself within your waking life. Swimming in murky water indicates an environment of negative, or depressive emotions.

6 - Represents teaching and service. Also, symmetry... unity of body and spirit, the visible and invisible, etc. Alternately, six is a multiple of three, and may symbolize conflict within the representation for the number three, which represents the trinity. It is an active or a process number (something is going on in the psyche). The number three may symbolize vision(forward thinking), completeness, and fulfillment. Also, anything that may contribute to your personal fulfillment for example, the resolving of conflict between two opposing forces.   

7 - the cycles of life, ie: 7, 14, 21, etc., a week,  transcendent meanings; 7 candles, 7 churches, 7 chakras, 7 colors of the rainbow, 7 notes of the scale, and so represents investigation into human wholeness, or seeking complete oneself.
 
Also, consider the term, "Sixes and Sevens", which symbolizes conflict, or confusion.

Alligator - This coldblooded animal could hold several different meanings in your dream. It could symbolically represent something from your memory, emotions, or a current situation or individual in your life. May symbolize a problem, responsibility or task in your real life that has troubled you a bit, and needs "wrestling", sometimes with the help of others.
Treachery, deceit and danger, as well as hidden instincts. You may be feeling that someone around you does not have your best interests at heart, and it might be someone whom you thought you could trust. Your subconscious may be warning you to be very cautious in business ventures, or to think before signing any contract or agreement. It may be a signal for you to take a new perspective on a situation.

May represent power of expression used in a destructive way (angry and hurtful words), or fear of misusing verbal expression. The power of the unconscious mind needing to express itself {repressed emotions}. Dangerous unconscious motivations that need controlling. This dream symbol should encourage you to look at some of your more "dangerous" emotions, memories, and experiences, hurtful and negative things being "swallowed" by the subconscious.

No fear of the alligators - suggests you feel as though you are aware of a problem, and that you see what you must do to take control, or that you know know who was causing your problem.
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Have you been dealing with a troubling situation in you life?
Is there someone who you feel has betrayed your trust?
Do you have a conflict with someone in your waking life, or within your 'self'?
Did you have an argument recently, and heated, or cruel words were exchanged?

Hope this gives you some insight, good luck!