① I'm not feeling well today. ：今日は体調が悪いです。
I'm not feeling wellは「体調が悪い」という意味です。この表現はよく使われています。
I'm sickにすると、症状が重い印象になります。
② I have a cold. ：風邪を引いています。
havea coldとcatch a coldはどちらも似たような意味ですが、have a coldは風邪を引いている状態、catch a coldにすると誰かに移されたというイメージになります。
ご参考になれば幸いです。
I'm feeling under the weather today. It's not for me
Under the weather = slightly unwell or in low spirits, ill, unwell, indisposed, ailing, poorly, not (very) well, not oneself.
"She was sufficiently under the weather to have to pull out of the championship."
Out of sorts = slightly unwell, unwell, ill, poorly, bad, indisposed
"She's been feeling nauseous and generally out of sorts."
Under the weather =少し落ち込んでいる、体の具合が少し良くない
"She was sufficiently under the weather to have to pull out of the championship."
（彼女は少し体調がよくなかったので決勝戦から手をひかなくてはいけなかった）
Out of sorts = 元気がよくない、意気消沈した
"She's been feeling nauseous and generally out of sorts."
（彼女は吐き気がしていつもより元気がない）
Thanks, but I do not think I will come. I am feeling a bit sick.
Thanks, I will have to pass. Not feeling to good today.
▪Thanks, but I do not think I will come. I am feeling a bit sick.
▪Thanks, I will have to pass. Not feeling to good today.
●
Example 1
Friend: We having a party later, you must join.
You:Thanks, but I do not think I will come. I am feeling a bit sick.
Example 2
Friend: We having a party later, you must join.
You:Thanks, I will have to pass. Not feeling to good today.
▪Thanks, but I do not think I will come. I am feeling a bit sick.
▪Thanks, I will have to pass. Not feeling to good today.
例 1
Friend: We having a party later, you must join.
You:Thanks, but I do not think I will come. I am feeling a bit sick.
友人: あとで私たちはパーティーをするからあなたも来なよ。
あなた:ありがとう。でも行かないと思う。体調がよくない。
Example 2
Friend: We having a party later, you must join.
You:Thanks, I will have to pass. Not feeling to good today.
友人: あとで私たちはパーティーをするからあなたも来なよ。
あなた:ありがとう。でも今回は具合がよくないからいけない。
I'm sorry I cannot be there because I'm not feeling well
Unfortunately, I won't be able to come because I am sick
When you're invited for a party but cannot go because you are sick, then you can say to the person:
-Thank you for the invitation but I can't come because I am sick.
-I'm so sorry I cannot be there because I am not feeling well.
-Unfortunately, I will not be able to attend because I am sick.
パーティに誘われたけれど体調が悪くていけない場合以下のように言うことができます。
-Thank you for the invitation but I can't come because I am sick.
お誘いをありがとうございます。けれど体調が悪くていけないんです。
-I'm so sorry I cannot be there because I am not feeling well.
ごめんなさい、体調が良くなくていけないんです。
-Unfortunately, I will not be able to attend because I am sick.
残念ながら体調が悪くて参加することができません。
Thanks for the invitation, but I am not feeling well today and cannot make it.
I got sick, sorry I cannot come today!
Thanks for the invitation, but I am not feeling well today and cannot make it. - This is a polite way to tell someone that you appreciate their invitation but cannot make it because you are unwell.
I got sick, sorry I cannot come today! - A very simple and to-the-point way of telling someone that you are sick and this is the reason why you cannot attend their gathering.
Thanks for the invitation, but I am not feeling well today and cannot make it.
（誘ってくれてありがとう。でも今日は体調がよくないから行けません）
- 誘ってくれたことに感謝しつつ、体調が悪いので行けないと伝えています。丁寧な言い方です。
I got sick, sorry I cannot come today!
（風邪をひいてしまって、今日行けない）
- 体調を崩して、参加できないことを伝えています。simple（シンプル）で to-the-point な（要点を押さえた）言い方です。
I wish I could go to the party, but I not feeling well.
I would love to go to the party but I am feeling a little sick.
"I wish I could go to the party, but I not feeling well." is a polite way to reject an invitation to a party while still insisting you would have gone if you were not sick.
I wish I could go to the party, but I not feeling well.
（パーティーに行けたらいいんだけど、体調が少し悪いです）
これは丁寧に誘いを断る表現です。
パーティーに行きたいんだけど、あなたは体調がよくないのでいけないという意味になります。
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