Essential oils are natural chemicals that are extracted from the leaves, flowers, stems, roots or bark of plants. They are the aromatic and volatile essences derived from botanicals.
Whereas, Fragrance oils (also called perfume oils) are usually synthetic; chemists analyze the plants’ components and reproduce their chemical compositions. Although essential oil blends (combinations of essential oils) are not synthetic, some suppliers call them fragrance or perfume oils.
Yes, both Lavender and Tea Tree essential oils have anti-fungal and antibacterial properties. Just be careful cause I know tea tree is especially dangerous ingested or put into ears. Make sure it is diluted properly, a good idea is to get a good book on Essential Oils. My favorite is The Complete Book of Essential Oils and Aromatherapy found here: book
Cinnamon, clove and Rosemary essential oils also have antibacterial and antifungal properties.