Your chances for college admission are certainly not lost. Junior year grades are very important, but remember my comment to Gigi above: college admissions committees are not full of robots.

You will definitely want to address your F in your application packet. Many universities will allow you to submit a short addendum (e.g. to discuss something about your file outside of the scope of your personal statement). Explaining the move from non-honors to honors and your difficulty with the move will help to explain your small lapse in grades. This approach will be especially helpful if you earned a higher grade in your math course in your second semester and in your senior year (make sure you keep working hard!)

If you know you're interested in a UC, you might also consider contacting the admissions offices of a particular UC you are most interested in to explain your situation. They can likely give you more directed advice unique to their program. While my tips will work for a number of schools, having a targeted answer from a specific school regarding a particular problem is always the best approach.

I want to close by asking why you are opposed to transferring from a community college. I know many students (and myself included when I was applying to colleges) feel like that route is "less than" a direct entry into a 4-year university program, but remember that spending 2 years at a community college and transferring into a university earns you the same diploma, will likely save you money, and may even get you into a better school. It may feel like a smaller achievement, but four years down the line, will make little difference.

Best of luck to you, Eshaan!