Advanced undergraduate courses will cover material that is fundamentally, qualitatively different from anything you've be exposed to - after the first year or two it will be about making rigorous inferences about the behavior of abstract mathematical objects just as often if not more often than performing computations and manipulating symbols.

It's hard. No matter how quick you've been in the past, it will throw you for a loop. The fact that you're used to taking your time to learn something in it's entirety will be a huge asset. Other students who have a history of picking things up quickly without having to really study or engage with the material will perhaps do very well for the first year or two, but your steadier more disciplined approach should allow you to catch up or pass them by eventually.

IMO, the first rule of learning advanced mathematics is don't be scared of it. You need to get comfortable being deeply, extremely confused, and putting together a working understand one little piece at a time. If you're not confused the majority of the time, you're not taking challenging enough classes, and you're not learning enough. Facing that confusion without letting it cause fear or anxiety is arguably the most important skill.

The second rule is not to take life advice from other people if that advice doesn't feel right. People who are good at mathematics are usually very bad at giving advice. They don't actually know which things they did in life helped them, so they rattle off a random bullshit collection of things they did, things they didn't do but thought about doing, things they think one of their friends did, etc.

On a more practical level, many people say that this is the best way to study: make a list of questions, concepts, and example problems that together make up all the material you're trying to study, and make sure that list does not include any answers or definitions, only names of concepts and questions. Go through one at a time, try to define each concept in your own words and solve every example problem without looking at your book or notes. If you can't, look up the answer or method, finish the problem, and mark it with a star. Note that these answers and definitions go on a separate piece of paper, which you put away or throw away immediately when they're done. When you get to the end of the list, go back and solve/define all the starred problems without looking at the book or notes again. Only un-star the problem if you solve it without the book or notes this time. Repeat (within the same study session) until everything is un-starred. Perform this process every day until you get everything on the first try.

Edit: one last thing. Some people think that a person has a fixed level of innate mathematical talent. Those people are wrong. Mathematical ability is like a muscle. Maybe some people lucked out and figured out a good excercise routine early on, and it makes them look like they have natural talent. But they've just been practicing efficiently. It's all about practice - that's where mathematical skill comes from. You fundamentally *do* have it within you to become excellent at mathematics if you put in the time and work both hard and efficiently. Figuring out how to work efficiently will take time and open-mindedness. Give yourself the mental and emotional space to grow and learn.