I think the series of books on elementary mathematics by Israel Gelfand would be absolutely perfect for you. There are four in total, but given what you'll have covered already, I would suggest you pick up Algebra, co-written with Alexander Shen, and Trigonometry, co-written with Mark Saul. They're written with a lot of care and full of exercises that will actually make you think, rather than just blindly compute. These books will, without doubt, develop your fundamental skills and they're also a lot of fun to work through.
Another one that's very good and, like the Gelfand books, written by an eminent mathematician, is Basic Mathematics by Serge Lang. This covers algebra, synthetic and analytic geometry, and trigonometry with a nice mix of computational and theoretical exercises. It's an excellent book, with a particularly interesting coverage of geometry based on isometries and dilations, but I think I'd rate it slightly below the Gelfand series. The difficulty level is also a bit lower in Lang, I'd say.
Finally, there are the translations of the Japanese grade 10 and 11 textbooks from Kunihiko Kodaira, the latter in two volumes (Basic Analysis and Algebra and Geometry), published as part of the 'Mathematical World' series from the American Mathematical Society. These are of an excellent standard, proving a far more interesting and logical development of school mathematics than their modern British or US equivalents, and don't seem to be nearly as well known as they should be. I believe the reviewer N.F. Taussig on Amazon describes them very accurately.
I've worked through all of the above books, with the exception of Gelfand's Trigonometry, which I'm currently in the middle of, and feel I've gained a lot from all of them.