@nina_online - In general, I'm very pro-vax and think the benefits outweigh the risks for most if not all patients.
That said, I have relapsed acutely twice from vaccinations - timing was quite clear - and in each case it took months to years to revert to normal.
My experience is that live attenuated vaccines do not cause problems. The dead vaccines cause problems - I suspect the issue for me at least is the immune overactivation caused by the body's reaction to the aluminum salt adjuvants used in dead vaccines. The live vaccines are more like a REALLY weak infection (weaker than a cold) - so I do not think they pose significant risk. I would definitely vaccinate for serious diseases. For flu, I think I'd do the inhaled nasal version as it's live attenuated and not killed and thus doesn't require adjuvants.
In my own body, I do have some understanding of what is happening. I have specific genetic markers associated with rare but understood diseases which prevent me from effectively resolving the inflammatory response. I have reason to believe these occur with significantly greater frequency in ME patients based on looking at 23andme data for about 30-40 patients.
Keep in mind this is all preliminary and not established fact - so take it with a grain of salt. I'm trying to give you the best info I can in an area where well supported scientific knowledge is meager.
Your doc may not be willing, but with heat killed vaccines, I would recommend being ready to downregulate the immune response if the reaction is bad (for example, dexamethasone, a corticosteroid that penetrates the BBB).
One ME doc I went to said that he did not recommend flu shots for his patients unless they'd had them before and not had a reaction. That might be a good gauge. Either way I'd recommend the live attenuated as safer. If you don't get a bad relapse or ME from each minor 24 hour cold, then it's unlikely you'd get anything from these extremely attenuated strains.
Dr. Byron Hyde (google - you can even read his book for free, which is like 1k pages) writes that a number of his patients had problems with the Hep B vaccine. This is not a live vaccine - it's not even inactivated. It's a recombinant subunit vaccine - which means there's no plausible way it can cause infection. They just take the genes for the outside of the virus - not enough to make a whole virus - and grow them in bacteria by transfecting the genes into the bacteria (recombinant tech). Hep A vaccine also uses a similar technology, as do the HPV vaccines (gardasil, cervarix, and the new gardasil-9).
I had the hep B vaccine in college a few years after I got sick, all 3 shots, and had no bad reactions, and since then have been tested and decades later have good immunity. I also had hep A vax in college and no adverse reaction. Whatever it is, it's not completely predictable. My grandfather nearly died from a tetanus shot - and they couldn't figure out why - although I might now be able to shed light on it based on some genetic studies.
This is a jumble of conflicting and partial info because I cannot give you a definitive correct answer - I don't think anyone can - but I thought I'd share what I know.
I would urge you to not underestimate the severity of the diseases that these vaccines protect against. There are reasons we have these vaccines. The diseases were horrible. I definitely would not skip vaccines for whooping cough, the MMR for measles/mumps/rubella, and a bunch of others that are very serious. Also, it's not unreasonable to hold off on vaccinating babies against diseases that they have almost no chance of encountering in the near future if you believe they are at elevated risk, but don't forget later! If a baby gets HPV that baby has bigger problems... that shouldn't happen. Similarly, Hep B is blood borne or sexually transmitted - similar to HIV, but actually much easier to spread, and can be fatal. Hep A is often acquired through food - so anyone can get that.
Talk to your doc though. Do not read all the crazy anti-vaxxer sites. If you didn't have a family history of ME, I would say the evidence is overwhelming that they are likely to be safe. Even with ME, I still get vaccines to this day because some of the diseases they prevent are simply too serious to ignore. Measles is NOT a joke and it is EXTREMELY contagious. This is why many pediatricians won't take patients who don't get the vaccine - once the sick measles patient comes to the office, there is infectious measles virus floating around for the rest of the day, at least, even after the kid is gone, and there are young children there who are too young for vaccines. So it's not safe for the other patients for pediatricians to allow an unvaccinated measles patient in their practice. Mumps causes sterility in men, and rubella causes birth defects. Any of them can, sometimes, kill. Chicken pox leads to a future risk of shingles - often many decades later. Those of us who had the virus and not the vax have low levels of activity of the varicella zoster virus for life (VZV or HHV3) - when the immune system weakens, out it comes.
I can tell you that each time I've had a vaccine I have recovered, even if it took a while. Recovery in my case is sped up by corticosteroids (dramatically). You can't take those right after a live attenuated - but your doc will know this and they are rx only.
Tricky decisions but don't underestimate the severity of the diseases against which we vaccinate.