There's nothing to worry about. Just finish as many of the tests that you can, and then send them off the results via email and explain the situation.
Just out of curiosity, which vaccination do you have to wait a month for? I did all my vaccination shots in 2 days, although not consecutive days (one day in December and one day in April, ha!). I'd walk out of the clinic with 4-5 bandaids on my arms.. it freaked people out a little I think, heeh
Anyway, I finished the entire process over 4 days. Your doctor should be able to administer the vaccines in a sequence which allows for the whole process to be faster..