It is definitely worth appealing your claim, since there is no cost to you, and it's possible that a judge would see your situation differently than EDD initially did.
You have 30 days to appeal your denial that you received on April 1st. On appeal, your employer will allege that you voluntarily quit your job since you didn't show up for work for a few days and failed to request a leave of absence or inform your employer that you would not be present.
Unfortunately, it will be difficult to counteract that argument, but since they only waited two days, it's possible that the judge would think that they did not wait a sufficient amount of time or took no steps to try to talk to you to ensure you were leaving work and were not ill or had other issues that prevented you from showing up for work.
Another thing potentially working in your favor is that you can have good cause for leaving your job if you do so due to marital problems (separation or divorce). Definitely, a physical argument for your spouse would be the kind of thing that would prevent you from working and you can argue that it was necessary to leave in order to deal with your marital issues.
I'm not saying either argument is necessarily a winner, but taken together they may provide a compelling case for you to receive benefits by either proving that you did not voluntarily quit your job, or if you did so, you had sufficient good cause to justify the voluntary quit.
Thanks and best of luck!