Can I work in a second job whilst off sick from my first Job?

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I am in the early stages of pregnancy with my 3rd little one and by the end of the day I am completely shattered. I work 2 night shifts per week with my first job and my second I manage a playgroup a few hours -3 days per week. I can just about manage my day job through throwing up all day but then the thought of going out at night fills me with dread as I can barely keep my eyes open after tea time. Is it possible to get time off sick doing night shift but continue to do my day job?

I'm not looking for opinions only facts. Thanks.

Can I work in a second job whilst off sick from my first Job?