Strep? Moderate cold, severe headache & sore throat for a week. Cold & headache improving, throat worse than ever. No fever. Yellow patches on tonsils.

Could be. It is easy to get a strep test and important to rule out as strep is an illness needing antibiotics. Flu cn also have similar symptoms...And it is not uncommon to have both flu and strep together. Yes- go and get a strep test. Strep can present with two or more of the following symptoms: headache, sore throat, fever, vomiting, diarrhea, rash, nausea, and stomach ache..
Possible Strep. Sounds most likely like strep throat, but could be mono if an older child, especially a teenager. Would take in to see the dr an get throat swabbed to know for sure and start medicatins if strep.