That’s a lot to unpack.

Yes, vaccines have very low concentration of compounds of those metals.

Yes, those metals at the concentrations in vaccines can cause minor side effects, though there is no evidence of serious side effects.

But, more to the point, vaccines more broadly than those ingredients occasionally cause serious injury. This is a rare but known risk.

> I not allowed to sue about that

It is true that one cannot sue in the US over vaccine injuries but presented alone in this context that is misleading to the point of dishonesty, since there is an alternative compensation program (one where, unlike with regular court where if you win you are still out legal costs without extra proof of particular egregious conduct, you can be awarded costs and fees even if you aren't eligible for compensation for actual harms.)

https://www.hrsa.gov/vaccine-compensation/index.html

That's because the “medical establishment” doesn't view vaccines as perfectly safe, but instead that they are viewed as being safe in the same sense as other prescription medicines but, further, than the public health establishment—the relevant part of the government—feels there is sufficient public health benefit from vaccination that even harms which would not compensable for other approved drugs are compensable on a no-fault basis for vaccines, to encourage their use.

> and no one in the medical establishment would acknowledge that the only cause of my daughters sickness could have been the vaccines.

If no experts would agree with your claims of causation, then allowing you to sue would just be allowing you to incur a bunch of costs to no end. A more likely explanation for no experts agreeing that the one thing you've focussed on as the cause being the cause is that there is not evidence for the claim of causation.

> There is propaganda about vaccines being harmless

There may be somewhere, but it's not coming from the “medical establishment” or the government, both of which acknowledge that there are both the common minor and less common severe harms from vaccines.