Recent advances have enabled automatic sound recognition systems for deaf and hard of hearing (DHH) users on mobile devices. However, these tools use pre-trained, generic sound recognition models, which do not meet the diverse needs of DHH users. We introduce ProtoSound, an interactive system for customizing sound recognition models by recording a few examples, thereby enabling personalized and fine-grained categories. ProtoSound is motivated by prior work examining sound awareness needs of DHH people and by a survey we conducted with 472 DHH participants. To evaluate ProtoSound, we characterized performance on two real-world sound datasets, showing significant improvement over state-of-the-art (e.g., +9.7% accuracy on the first dataset). We then deployed ProtoSound's end-user training and real-time recognition through a mobile application and recruited 19 hearing participants who listened to the real-world sounds and rated the accuracy across 56 locations (e.g., homes, restaurants, parks). Results show that ProtoSound personalized the model on-device in real-time and accurately learned sounds across diverse acoustic contexts. We close by discussing open challenges in personalizable sound recognition, including the need for better recording interfaces and algorithmic improvements.