There are several synonyms for the phrase "blowing one's own horn" that can be used. These include boasting, bragging, tooting one's own horn, talking oneself up, self-promoting, showboating, and self-aggrandizing. All of these words can be used to describe someone who is excessively praising themselves or their talents, often in an attempt to gain attention or admiration from others. While a certain level of self-promotion can be healthy and necessary in some situations, it is important to strike a balance and avoid becoming too overbearing or narcissistic. Alternatives such as humility and modesty can also go a long way in building genuine relationships and earning respect.