Lady Justice is blindfolded because justice is supposed to be blind. A person's past run-ins with the law do not make him or her any less injured, and that same past does not make the at-fault person any less responsible for the harms caused. So why should it affect your case?
In most cases, criminal history will not affect the case. There are rules that are intended to secure that justice is blind for people with past convictions. With few exceptions, the other side is not even entitled to learn about it in discovery. They can only ask about information that is reasonably calculated to lead to the discovery of admissible evidence.
Evidence of criminal history is only admissible to attack a person's credibility. In other words, the other side can introduce it to try and show you are not telling the truth about an important aspect of your case. Because of that limited purpose for which it can even be introduced, the criminal history at issue must either be a felony or be a “crime of dishonesty.” These crimes usually involve theft or lying as an essential part of the case.
In Washington, the court can still exclude the conviction if the danger of unfair prejudice outweighs its relevance. Also, if the conviction for anything other than a crime of dishonesty occurred more than ten years prior to the time of testimony, it is not likely to be admissible. In Oregon, the date of conviction must be within the past fifteen years to be admissible. In both states, convictions are not admissible if they have been expunged, pardoned, reversed, or otherwise set aside.
Another consideration is just how a jury would view the conviction. You would have a brief opportunity to explain the circumstances, and the jurors could assess whether they thought you were telling the truth about your injuries generally. Hopefully, your testimony, combined with statements and other evidence from your medical providers, family, and friends, would combine to overcome any potential bias the jurors would have due to the criminal history.
I like telling people that the case is the case. People with and without criminal records get hurt. If you are unlucky enough to have one of the admissible types of criminal convictions, be mindful of what you are saying and how it might be perceived by both the jury and the other side. So long as you don't try to stretch the truth on what happened during the event in which you were hurt, and just how hurt you were, your criminal history should not have too big an effect on the case, if at all. There are ways to overcome the challenges a criminal history presents. That starts, first and foremost, by being truthful about your case and not running from your past. Even if justice is not always truly blind, the truth will win out.