I wanted to make up the fasts I missed during Ramadan straight after Eid. I celebrated Eid yesterday and kept a fast today. however, I have read now read online that I should not have fasted the first 3 days after Eid. Will my fast still be accepted?

Your fast is valid only on two Eids (Al Adhha and Al Fitr)it’s Haram to Fast on that day otherwise rest of the year having other conditions of Fasting on can fast.