It's a correct sentence. Showing that those two events happen at the same time.
Is 2 the same as 1? I mean two events at the same time. Maybe to make it more clear I should've said "If I am being sick"
'Grammatically correct' only means you have the sentence structured correctly. It doesn't always mean they are logical or idiomatic.
Your sentences don't refer to two events happening at the same time - they seem like conditional statements. In other words, you're saying that if one thing happens then the other will be true.
Although you likely have gone running in the past, and perhaps she slept while you did so, a conditional statement about running and sleeping just doesn't sound right. It's not logical or idiomatic, for a few reasons.
Conditional statements with 'if' and 'then' usually mean that one thing happens as a result of the other. Your running doesn't cause her to sleep. Conditionals are also for possible situations, but it sounds like this is something that actually happens on a recurring basis.
It would be best if you used a temporal clause:
A temporal clause indicates the timing of an action relative to another action and can describe recurring events, habits, or routines.
Your other example could be either:
This is because being sick is only a possibility rather than a regular, expected event; however you could also view it as an inevitability, because everyone gets sick from time to time.
