Hi Korey!
Having botox be a few days late is probably not a huge deal, I would think. I got screwed up when it was a month late, but my doctor's office has to adjust my injection date a few days here or there all the time due to scheduling and as long as it's just a few days, I've personally never noticed a difference. Maybe other people will jump in with their experiences.
I linked an article below that discusses MOH in depth, but when taking any acute medication (triptan, narcotic, simple analgesic like tylenol or aleve), I believe 2-3 times per week, for fewer than 10 days total per month are the current recommendations. Some medications are the heavy hitters with MOH (anything containing a narcotic, triptans). Simple analgesics are considered lower risk to cause MOH than narcotics and triptans, but yes, will still cause it.
I was always careful to stay under the 2-3 times per week rule, but I have chronic migraine, so was using triptans with tylenol or advil month after month and eventually got into a MOH cycle anyway, which sucked. My neurologist pointed out that the rule on how many times per week is a guideline and every body is different. It may only take 8 doses per week for one person's body to go into MOH. Another person might take 14 doses and be fine. I had to listen to my body and notice that it was taking more medication to stop the migraines (when they stopped), that the migraines were always rebounding back the moment the meds wore off after so many hours, and to keep a careful migraine/medication calendar so I chart back and realize something was wrong.
https://migraine.com/blog/help-how-can-i-not-overuse-migraine-medications/