OK this is a question that no-one here can answer because they do not know you, they have never heard you sing and they do not know how much effort you are putting into getting to the top/bottom of your range at the moment.
Pushing your upper limit further has the potential to be dangerous and/or damaging; you need to take the advice of a professional ...
The physiology behind speaking and singing is the same, which is why you haven't been able to find separate answers for acting. It's all vocal physiology. All of it uses the human voice. Singing could also be described as sustained-vowel speaking, which is what is happening in the videos you posted.
Your vocal fold tissues are still inflamed from your sinus issues.
The main muscles involved in phonation are the vocalis, the crico-thyroid, and the thyro-arytenoid.
In a recovering/inflammation situation, the mid-range is the last to come back. Cancel the gig, hire a sub, but don't try to sing a 4-hour gig in two days. That will just make it worse. Allow ...
The answer is right there in your first sentence... "recovering".
Once you've actually recovered, you'll be fine.
No good trying to rush it & push it, you'll hurt something if you're not careful.
Cancel the gig.