Do prozac and lexapro (escitalopram) work the same way? which one works best for treatimg depression and anxiety?

Essentially yes: They both work. Lexapro may have less associated side effects but stronger serotonin effects (so more serotonin side effects can be seen with lexapro). Lexapro was developed to get rid of the bits of proxac/ Paxil (paroxetine) molecules which cause other organ side effects. Side effects are still similar even if lessened. For sure, Lexapro seems to have less interactions with other medications.

SSRIs: Prozac and Lexapro (escitalopram) are ssris for the treatment of depression. Lexapro (escitalopram) is also approved for treating anxiety, panic, and ocd, as well as in treating autistic spectrum disorders such as asperger's. While both medications are similar, the molecules are still somewhat different.

MEDICATION: Best to discuss medication with your Psychiatrist. If uncomfortable with your Dr. consult another for a second opinion. Have a physical exam by a Dr. to determine if you have a physical illness. Consult with a Clinical Psychologist for psychotherapy with ZOOM sessions. Fears and anxiety could be heightened due to the Covid-19 pandemic. Stay safe & hopeful to elevate your immune system.