I thought you said it was doxycycline? Doxycycline is not contraindicated in lupus its actually often used to treat arthritis flare ups, the only abx that should be avoided are sulfa containing ones and caution with penecillin so your GP would have been right in prescribing it
Also the main reason doxycycline is contraindicated in pregnancy is because it can affect foetal bones and teeth so its actually the last 2/3rd of preg its a real prob, its considered usuable in the 1st 16 weeks. And like we discussed last night if its a one week course you will be finished the course before you even implanted were you to get a bfp this month so again not a reason to not take it neccesarily.
Lastly vomiting is a common side effect of many antibiotics, its not generally a good reason to discontinue them. The best way to prevent it is to take it on a full stomach, if you cant take it with food have a glass of milk to prevent gastric irritation.