Yes, it’s absolutely possible. In fact, many people with candida don’t have oral thrush. If you have other symptoms like upset digestion, fatigue, yeast infections, then it’s totally possible.
Antibiotics are not designed for Candida, and they will in fact make it worse. Beating Candida is not a quick fix, it needs a plan and a long-term commitment. The change in your diet is the most important. You can find lots of information on this website and in the book. Cutting out added sugars is the biggest, more important step. Then you can think about probiotics, antifungals, etc.