Am I good to apply now? UCLA?

Hey, so this is my first post to this site. I have been a premed student for two years, and honestly never knew about this site.

Anyway, I am currently a sophomore at my university, but I graduate next fall in molecular bio and microbio major. I am 20 years old, so a lot of students have said that I am too young to apply. However, the doctors I have spoken to and even residents have said that I can apply now, even though I am 20. I'll be 21 this upcoming summer.

Should I apply to medical school?
Do I have good chances right now for ANY allopathic medical school?
UCLA is my top choice, do I even have a chance?

Here are my stats:

• Research: Research assistant for 4 years at my medical school lab. Started in high school. Have a biomedical patent and finished my honors thesis. Have conducted several projects at the lab and gained several research skills. My research involves tissue engineering, biomaterial synthesis, stem cell (iPSCs/hNSCs/ADSCs), and Alzheimer's treatments with a multifunctional drug I patented. I also presented my research at a showcase of undergraduate research. I am currently in the process of publishing my paper.
• Volunteering: Volunteered at a hospital for 50 hours. ***I had to stop for personal reasons. I also gained enough experience after about 25 hours to be honest. I also volunteered at my county's high school science fair as a judge for medicine and health, biochemistry and chemistry divisions for two years. (I became a judge after I placed 4th in the international science and engineering fair for medicine and health sciences my senior year of high school).
• Shadowing: I shadowed a radiologist and a dermatologist. I plan on shadowing my doctor, but he said I will not actually be with him seeing patients...so not sure if it is worth it. I may shadow a pediatric neurologist.
• Leadership: I have been a director for my premedical club for two years. I have gained several leadership, communication, and presentation skills from this position. I was also a leader of several projects in my lab.
• MCAT: Will take an MCAT prep class and see how I feel. If I feel good about the MCAT, then I will take it this May. If I don't feel good about it, I guess I'll do a gap year and in that gap year I'll do an internship at the NIA.
• GPA: I have a below avg GPA. The avg applicant GPA is around 3.7ish. I have a 3.6 around there.
• Rock climbing club at my university. Competed in several competitions. 5K runner.

***I did suffer from major depression, which impacted my grades greatly one semester. I am not sure how I explain this to medical schools. It really makes me think that medical school isn't for me. However, I did perform well the following semester with As.

If you need more info, please ask. I can provide you with the information.

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Am I good to apply now? UCLA?