Ask a Dentist. Get Answers to Your Dental Questions.
Thanks for putting up your question on Just Answer.
The flight is not a problem, but the vacation might be. The doctor has prescribed an antibiotic, which will bring down the infection, but that may not be enough.
What is required is some dental procedure. The loose tooth needs to be extracted. This is really bad timing for this to happen hours before you are scheduled to go on vacation. The safer thing would be to get your tickets postponed by a few days and extract the tooth in your city itself.
Hope this answers your question. Feel free to contact me again for more information. Please leave a positive rating for me if this answer has helped you. I do not get credit for it otherwise.
Good Luck !