These two sentences are great ways of expressing that you have sensitive skin. In the second sentence you will see the word susceptible. Although this words has different meanings in this sentence it means likely to be harmed of affected by a particular thing. So, if there is something in particular that makes one's skin sensitive, like the sun, they can use this word to explain that their skin is sensitive and why.
Depending on what specifically makes your skin sensitive, you can use one of these to find a more specialized product for your skin:
Dry skin is when your skin lacks moisture, often times after the shower or washing your face.
Oily skin can cause frequent acne or blackheads.
Combination skin is when you have a mix of both dry and oily skin.
It depends rather on why your skin has accentuated feeling and whether the effect is painful or not. If the skin is generally affected by creams or chemicals, or perhaps sunlight, then it may be said that you have sensitive skin. If, for example,you suffered a burn or have inflammation or injury such as having been scalded by boiling water, then the skin would be described as 'tender' in that case.
"After doing the dishes, I put on a special hand cream for sensitive skin."
これは、むしろ肌に痛みの症状があろうとなかろうと何故肌が刺激を感じるのかによります。肌が、もしクリーム、化学製品、または太陽の光に概ね影響されるなら、sensitive skin（敏感肌）だと言えるでしょう。
例えば熱湯などによって、やけどを負う、炎症、または負傷すると、この状態の肌はtender（敏感な、触ると痛い）と言います。
例：
After doing the dishes, I put on a special hand cream for sensitive skin.
お皿洗いをした後、敏感肌用のスペシャルハンドクリームをつけます。
"My skin is quite delicate." Delicate means that it easily gets damaged and is to be handled carefully.
"My skin is easily irritated." means that the skin reacts easily to different irritants and hence it means the skins is sensitive.
"My skin is quite delicate."（私の肌はかなり敏感です）
Delicateは、ダメージを受けやすく、気をつけて扱わなければならないことを表します
"My skin is easily irritated."は、肌が色々な刺激に対してすぐに反応してしまうことを表します。つまり、肌が敏感だという意味です。
Sensitive skin is skin that is susceptible to damage. You can use this phrase in the following ways:
-I have very sensitive skin, so I cannot use harsh cosmetic products.
-I'm very particular about the cosmetic products I use because I have sensitive skin.
Sensitive skin'とは、ダメージを受けやすい肌のことです。このフレーズを以下のように使うことができます。
-I have very sensitive skin, so I cannot use harsh cosmetic products. (私の肌はとても敏感なので、きつい化粧品を使うことができません)
-I'm very particular about the cosmetic products I use because I have sensitive skin. (敏感肌なので、自分の使う化粧品にはすごく気を遣っています)
ご質問ありがとうございます。
・「sensitive skin」
（意味)敏感肌
<例文> I have really sensitive skin so I have to be careful whenever I apply make up on my skin.
<訳> 敏感肌なのでメイクをするときは気をつけないといけません。
参考になれば幸いです。
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