Get the most out of your warm-up with Amsel
With time and repetition, your range will increase. Make sure you don't strain to reach those more extreme keys in the exercise. It's better to skip to the next exercise than to force your voice.
While it may be tempting to bump yourself up a level higher to see what new exercises await, it is much better for good development to do many repetitions of exercises that are too easy and to focus on good singing form than to take on exercises that may be more "intellectually engaging" but are beyond the coordinations of your voice and body.
If you've been around singers for any amount of time, you've probably encountered the famous "lip bubbles" or lip trills. These and other semi-occluded (or half closed) exercises (vvv, zzz, pursed lips, etc.) are essential for training proper breath pressure - not too much, and not too little. Every session with Amsel includes at least one of these. If you struggle with lip trills at the beginning, feel free to choose your favorite half-closed position (tongue trill, vvv, etc.).
The Amsel App, while a very powerful tool, is not meant to comprehensively teach singing. Just like serious athletes consult with personal trainers, developing singers get frequent personal feedback from voice teachers. Every voice has different natural attributes, and everyone develops different habits over time. Voice experts can give more exact feedback about your personal singing.