As someone who came into UCLA as an eighteen-year-old junior thinking I could handle two honors classes and was quickly humbled, I'd like to think that having found the bottom of the barrel, I can speak to incoming transfers about how to make their first quarter more productive than mine. I'll also give some of my thought process so that you can compare yours against mine and see if you're on the path to destruction as I was.
Please note that though I am using my experience as something to learn from, I do not regret taking two honors classes at the same time. It was a much-needed ego deflation and learning of my limits, and it also led to opportunities that I would not have had without taking those particular classes: in particular, it allowed me to speedrun the foundations of linear algebra and analysis required for other classes that I now enjoy. However, it did lead to unforseen consequences, including a dive in GPA, and I hope my experience will help clarify your sight ahead.
This is especially applicable to transfers to UCLA or other difficult schools who are diving straight into upper division courses.
Before I transferred in, advisors highly recommended taking a lighter courseload. "Do you have competitive math experience?" one advisor asked me after I presented my plan to take honors linear algebra and honors real analysis simultaneously. Unless you're like another transfer I know who finished lower-division classes for his physics degree in one year and entered UCLA taking six classes—and still has his 4.0—or a Math Olympiad gold medalist like Terry Tao, listen to them. Consider deeply that advisors have seen people, perhaps confident like you, who turn into crash and burns. If you doubt as I did whether there is anything significant needing much adjusting to, here are multiple things to consider.
Sleep. You will need a lot of sleep trying to learn math, since you are trying to teach yourself to interact with concepts in a new way and sometimes change how you think. Especially if you're new to proofs, which is a much more structured way of thinking, this is true. Caffeine is a poor substitute for sleep since sleep helps internalize ideas, but caffeine will just make you more focused. If the base is not there, caffeine will not build it. Realizing this gave me a sense of calm and justified rest, especially being a somewhat workaholic, since I needed to get sleep to do well in my classes. Especially if you get stressed if you are not doing work, this realization is something to internalize. If you have time, a nap right after a difficult concept also helps your mind mull over the details. One of the most enriching weeks of math was when I was sick; I would fall asleep trying to figure out topology lemmas, wake up, and having untangled some details, keep reading. Breaks and walks are excellent as well.
On the other hand, another of the most enriching weeks of mathematics was when I went to office hours almost every day. Studying alone is good for internalizing things, but going to office hours is HIGHly important for learning math and dissipating misconceptions. I realized this during fall quarter. The people who were doing the best in the class were the ones who were asking questions in class, and though I thought that they would not be going to office hours, on the few times that I did have time to go, there they were, badgering the professor with questions and boldly laying bare their conceptions to the professor. Perhaps it is a irrational fear or that we want to show our best traits to professors. At least for me, the cause of not going to office hours or asking questions in class was pride. If you expect to understand concepts immediately, dispose of that idea before even stepping foot on campus. I had this idea that I was supposed to understand mathematics if I did enough problems in it; and that is true; but that idea kept me studying alone without asking for help because I knew that I could get it if I just put in enough time, just did a few more problems, until it was dark outside. That mass of problems may not be what you have time to do. Going to office hours clears up questions so much more quickly. Be willing to be vulnerable to showing that you do have misconceptions. It is uncomfortable, and you may be humiliated when you realize how twig-like some stump in your head turned out to be, but the exorcising is worth it.
Coming into proof-based math, I had accumulated stories of what it was like: trying to figure out a proof to a problem—on the bus on the back of a receipt or waiting for food to be ready—and the eventual rush of joy when it's finally figured out after a sleepless night. This is not the whole of doing mathematics. This long-drawn-out tactic works in lower-division courses when you have time, but poring over trying to rediscover math proofs for hours alone in an empty classroom on a chalkboard is poetic but perhaps not the wisest use of time. How my TAs put it is that there is so much math that has already been discovered that pretending it is not there would set mathematics back several centuries. The greats like Isaac Newton who put days of time into solving some stuff and were heralded for it also had to study and learn from the tactics of others. Don't be ashamed to look up solutions to problems, and don't be ashamed to memorize the proofs. Though thinking through problems independently is a big part of learning to do math, you have to learn to think in a structured format correctly, from good proofs.
Ultimately this is practice in being teachable, being receptive to letting people into your mind when you might have misconceptions, and being willing to listen to what they have to say. Mathematics is better done with others. If you understand this, then I give you my blessing to sail into your upper-division courses. Make sure to consider wisely the balance between doing math alone and with others.