I was accused of a crime and held in custody for 8 months then acquitted at court, I missed the first 8 months of my only child's life, and lost both my job and my partner. Could I be entitled to compensation?
In all but a few U.S. states the answer is that you are not entitled to any compensation. This is grossly unfair, but is the dominant rule by far in most jurisdictions in the U.S.
As a matter of legal doctrine this is justified on the grounds that a criminal prosecution requires proof beyond a reasonable doubt, and many people who are actually guilty may be acquitted anyway because the standard of proof in a criminal case is so high. The classic example of that distinction is the O.J. Simpson murder case, in which O.J. Simpson was acquitted of murdering his wife in a criminal prosecution, but was found liable for murdering her by the lower civil action preponderance of the evidence standard in a wrongful death lawsuit brought by her family.
(In reality, most acquittals involve juries who think that the defendant was innocent, but that isn't reflected in the choice before them to convict or acquit a defendant.)
The only compensation to which you are entitled as a matter of law if you are acquitted of a crime, per the U.S. Supreme Court, is a refund of any fines or costs payable only upon conviction of a crime, which you paid or had taken from your assets, prior to your acquittal. See Nelson v. Colorado, 581 U.S. ___ (2017).
There would an exception if you can show that a law enforcement officer intentionally brought charges without probable cause in a civil lawsuit you bring against the law enforcement officer, which is realistically impossible in almost all cases. (Prosecutors and judges and jurors (see, e.g. here)) have absolute immunity from liability for their official acts related to the court process.)
There are a few jurisdictions where you could bring a civil lawsuit for compensation based upon "actual innocence", rather than law enforcement misconduct. In those places, you could receive compensation if you could prove by a preponderance of the evidence (or with a prosecutor's affirmation) that you were actually factually innocent, so you could get some compensation even in the absence of an intentional violation of your civil rights. Texas is one state that has such a scheme, with important limitations, as explained in this linked case.
You would probably have to hire a lawyer with your own funds to bring either kind of lawsuit, and realistically, you wouldn't have been incarcerated for eight months pending trial if you had enough money to do that, because you would have posted bond and been released pending trial.
There may be one or two states (I can't recall any from memory) where there might be a right to compensation merely because you are acquitted, but this would be an extreme outlier in terms of U.S. law.
Outside the United States, outcomes could vary dramatically from one country to another. They relevant law in England and Wales is discussed in an answer to this question at Law.SE. International human rights law does not recognize a right to compensation in these circumstances.