Question: “Can I refer to myself as buddhist if I don’t believe in reincarnation but I still live my life by Buddha’s teachings? And also is it considered a religion or a philosophy?”
Eeeh, not really. A major understanding of Buddhism is the teaching of death and rebirth; reincarnation. But why even refer to yourself as Buddhist? I know more non-Buddhist who practice Buddhist teachings than I do Buddhists! It shouldn’t be something your doing for the title, otherwise it is not genuine Buddhism. Buddhism isn’t about name or fame, titles or beliefs – it is the compassionate practice to liberate ourselves from ignorance, greed, and anger.
Buddhism is both a religion and a philosophy. It is also a way of life, it is music, liberal arts, ethics, and psychology. The Buddha taught his followers many things; proper hygiene, medicine (taking care of ourselves with it), exercise, and micro/macro management. Buddhism is many things. But like calling yourself Buddhist, Buddhism doesn’t need a title either.
Smile and be well!