Food allergy/intolerance or teething??

My DD is just over 4 months ebf and we got the ok to start cereal and such. We started her on oat. She normally poops once every 6-8 days. On the 3 day of oat cereal she had 2 poops(regular) the next day 2 poops, the her poops started being very green, sorta stringy and watery. No blood tho. She was still was feeding fine from breast and having wet diapers. Also around the 3 day she got very fussy which is out of the norm and her temp was up slightly, hands constantly in her mouth, tons of drool and wanting things on her mouth. You could see her teeth but nothing poking thru yet. After two days of that she settles back into her normal temperament and sleep. She got a rash about her face (a bit red and small bumps) and she got a pretty nasty rash on her bottom that I figured was because of the weird poops. I’ve tried to do some research but everything is a symptom of everything lol. It’s frustrating because I can’t figure out if the symptoms were due to teething or food allergy/intolerance? Should I wait a bit then try the oat again to see if she gets the same symptoms??