How to check if my string only numeric

You could use Regex or int.TryParse.

See also C# Equivalent of VB's IsNumeric()

Just check each character.

bool IsAllDigits(string s)
{
    foreach (char c in s)
    {
        if (!char.IsDigit(c))
            return false;
    }
    return true;
}

Or use LINQ.

bool IsAllDigits(string s) => s.All(char.IsDigit);

If you want to know whether or not a value entered into your program represents a valid integer value (in the range of int), you can use TryParse(). Note that this approach is not the same as checking if the string contains only numbers.

bool IsAllDigits(string s) => int.TryParse(s, out int i);