100.3 fever, sore throat with white spots, headache, nasal congestion. i have amoxicillin but i just threw up. still strep throat? mono? or another?

Yes, yes, yes: Yes this could be strep ( i assume you were tested for that as you are on amox), but it could also be the other things you mention including the "another". The rapid strep tests can has cross-positives on occasion with someone who has mono, or you could have a virus and just be a strep carrier. If it's been 3 days on the antibiotic, or you can't keep it down, time to call the doctor back.