This Iis Wwhy I'll Nnot Attend Aa Congressference

In English, "Congress" almost always means「議員」か「議会」.
"Conference" = 「会議」

I'm not a doctor but I often enter to operation rooms and advice how to use our products.

Alternatively: "... I often enter into operation rooms..."

We will have a congress of our speciality fromference about our (?) tomorrow, but I'll no won't attend it.

I'm not 100% sure what you mean by "specialty," but my guesses are either:
"product" = 「物産」と思う
"specialty product" = 「名物」

If you meant a type of "people" by "specialty", then my guesses would be:
"expert" = 「博士」
"specialist" = 「専門家」
But then the correct sentence would be:
"We will have a Conference with our experts/specialists tomorrow..."

However, it will be no problem.

"However, it won't be a problem." is a slightly more natural phrase.

I have a more important thing.

"I have something more important" is a slightly more natural phrase.

Actually, wWe are expecting a second baby right now, and the due date is coming soon.

"Actually" doesn't make too much sense here when coming from the previous sentence "I have a more important thing."

You could say "We are actually expecting a second baby..." (but the difference in meaning is very nuanced and hard to explain).

I hope my wife and new baby will be safe forduring the delivery.

My daughter really wants to caretake care of a new baby.

I wish tohope they get along.

In English, "wish" is very different from "hope". From the many times I've made this correction, it seems that "wish" and "hope" are often confused for Japanese speakers. I googled this question, maybe this blog post makes sense? https://www.qqeng.com/blog2/study/difference-wish-hope.html

I'm not a doctor but I often enter to operation rooms and advicese on how to use our products.

We will have a congress ofmeeting about our speciality from tomorrow, but I' will not be attending it.

"Congress" feels like a bit of an unnatural term to use here. I'm not entirely sure what you mean by "congress of our speciality".
"Meeting" is likely the term you were looking for.

"I'll not attend it" sounds a bit like a British person refusing to attend, rather than a simple statement of fact. Here it is very common to use the future continuous tense ("I will be VERB-ing"). When these sentences are negative contracting "I will" to "I'll" feels quite British - it's not wrong, but a less common construction.

However, it willon't be noa problem.

"will be no problem" isn't wrong, but this construction is more common and natural here.

I have asomething more important thing.

As above, the original sentence isn't wrong, but this feels most natural to me.

Actually, wWe are expecting a second baby right nowcurrently, and the due date is coming soon.

"right now" might give the impression that you're in the room waiting for the baby. It's not wrong, though.

I hope that my wife and new baby will be safe forthroughout the process of delivery.

My daughter really wants to care for the new baby.