Jalapeno peppers are very healthy for you and when eaten in moderation can fight off diseases such as cancer and even boost your immune system.
But yes eating too many Jalapeno Peppers can be harmful to your health because when you eat too many Jalapeno Peppers or even other spicy foods the hotness can eat away at your stomach lining and lead to stomach problems and even Ulcers.
Just eat the Jalapenos in moderation and if your stomach begins to hurt as a result of eating the Jalapenos then you should slow down on the Jalapenos until your stomach feels better.