Hi there littlemissp, and thanks for your question. When people talk about the interactions between medications, its about the active ingredients in those medications interacting with each other. Instead here what we're looking at what seems like the side effect of the antibiotic (diarrhea and vomit, sorry to hear that you're having this uncomfy time) and your pill.
Diarrhoea and vomiting comes with the risk that your body isn't getting the full dose of your pill because it is being passed out of your body due to the diarrhoea/vomiting so quickly. So those days where you did experience this can be thought of as sort of missed pill days, as the risk your body didn't get the full dose is high, and therefore you don't need to have a concern about your level of protection in the days prior to the diarrhoea/vomiting starting.
What you need to do if you will be having sex on days where you're having these episodes is to use a backup method of contraception (eg. a
condom, and also for a week after the symptoms subside.
It could also be a good idea for you to see your doctor and tell them that you're experiencing vomiting and diarrhoea with the amoxicillin, they may be able to help you by changing your antibiotic or giving you methods to reduce this happening.