@MoniDefi
My understanding (and it is not official) is that you have to be physically present in the country of issue to obtain the international drivers license. I agree with the post that online offerings have a high degree of probability of being a scam to steal your identity. AAA is the only place I know of in the U.S. to obtain the International Drivers license.
I just took the practical test in Spain. It took 6 classes and two weeks plus I drove my car around the projected test route and practiced parking plus all the little tricks one needs to be aware of to pass. Even though I have been driving for 55 years, I had some habits that did not conform to the standards of the test. For example, ALWAYS having two hands on the steering wheel...I had 4 points--out of 10--taken off for failure to have two hands on the wheel and I didn't even realize I was in "violation".
I overcame the language issue by learning the appropriate directions the examiner would give. Using a translator app on the phone to communicate with the instructor. At times she would draw diagrams on paper which was helpful. Doing a critique after every lesson and translating it on paper so the teacher could read it the following lesson and understand my specific problems and needs.
I was up against the 6 month time line as well...and had two weeks remaining. Having the international drivers license doesn't negate the 6 month rule as far as I know.
My personal feeling was as long as I could show proof that I was enrolled in a school (receipts if I was stopped) I was showing due diligence... I was stopped once at a checkpoint and my U.S. drivers license was satisfactory.
I have read that it is about a €200 fine if the police issues a citation. That's cheaper than a plane ticket back to the states to get a license that might not even be recognized in Spain for residency purposes.
Some other options you may want to consider:
Change driving schools to one that can schedule you earlier.
Change cities to obtain the license... your theoretical exam is transferable to other offices. A smaller city or town with less traffic and road complexity may be easier to learn in.
If learning to drive with a manual transmission is an obstacle, find a school that has an automatic transmission car to train in.
Take as many classes as you can and practice as much as you can before the 21st deadline to acquire skills and familiarity.
Don't be desperate.... take one day at a time... it's a process... relax... think of it as a game you are playing.
Wishing you peace and success... Hope this was helpful.