Will my Brother get Strep Throat?

Patient: I have strep throat. I went to the doctors and was prescribed antibiotics. The day after, my brother got sick and has a fever 100-102.5. He also is vomiting (i didn’t vomit) , has headaches, pain in his throat while coughing, and is coughing a lot . Then today, after coming out the shower, he used my towel by accident (same color as his). And I had used my towel when i had strep throat. Two hours later, he went to the doctor and got tested for strep throat, but it was negative and he didn’t have it. But was this too early to catch my strep throat? Will he get my strep throat? Should and when should we go to the doctor again?

Symptoms: coughing, throat hurting when coughing, vomiting, headache, fever