My body hads a new problem,it. I was beginning to cough yesterdaylast night, and I felttoday I had a sore throat today. My body has a new problem. I was beginning to cough last night, and today I had a sore throat.

"yesterday night" isn't really said, usually it's last night. It's unusual in English to refer to your body separately to yourself, so I changed "it" to "I"

It shcould be that it has started to get inflamed again. It could be that it has started to get inflamed again.

Should implies that something is the correct way to be. You probably want "could" here, which is about possibility.

It's too difficulty to for me into pronouncinge words, and speaking has becaome a challenge that wais hard to achievovercome. It's too difficult for me to pronounce words, and speaking has become a challenge that is hard to overcome.

Difficulty is for talking about quantity as a concept, when talking comparatively you should use difficult. Another alternative is "It's causing difficulty for me when pronouncing words". The changes to the second part of the sentence are to match tense with the first part.

I started to try to be a mute. I started to try to be mute.

"a mute" as a noun on its own is slightly insulting to mute people, so you should avoid using it. If you're talking about someone with medical muteness, you can say "a mute person", but if you're just talking about your temporary condition, it's better to just use the adjective form.

I found it was not bad to be a mute. I found it was not bad to be mute.

I didn't have to talk every day and doidn't get tired. I didn't have to talk every day and didn't get tired.