Not sure how to express this situation
Solution 1:
There is nothing wrong with just saying my older brother—or one of my older brothers. Both of those statements will always still be true.
But if you need to specify one older brother as opposed to the other, you can do so by using their name or by saying something like:
my older brother who is the closest in age to me
the youngest of my older brothers
my second-oldest brother
Solution 2:
One solution would be to describe him as
my next oldest brother
Google Books reveals plenty of uses of this exact expression in the sense of "immediately older".
Note however that this usage of "next" relates to the order or sequence of things, and its interpretation is therefore highly context-dependent.
next
adverb
in the time, place, or order nearest or immediately succeeding
- next we drove home
- the next closest school
If you haven't already mentioned a brother, then my next oldest brother would usually be interpreted as "the brother nearest in age older than me", exactly as you intended. However, if you've already referred to a brother, then this creates an ambiguity, since next oldest could also be interpreted as the following brother in the family order.
For example, if you have five brothers of which three are older than you, and you've already referred to the most senior brother, then "my next oldest brother" is likely to be interpreted as the second oldest of the male siblings, rather than Brother #3. Indeed, if you've already referred to all three older brothers, then "my next oldest brother" would logically be Brother #4 who, in this example, is actually younger than you!
Solution 3:
My inference of the statement is as below: "I have 3 brothers and I am the 4th child"
To refer to the brother immediately older than me: Can we use "My elder brother, who is younger than the other two"
OR
"The 3rd child, who is elder than me"
PS: Mods, comments (if any) with detailed explanation.