One option (probably simplest but not best) is to just increase the amount of memory your JVM is allowed to use, using the
-Xmx option.
Since memory is your problem, and that initial String is a big part of it, I would try to get rid of that String as soon as possible. My first choice would be to change the outside code to give you a Reader rather than a String. It's a bad API that forces you to keep all the data in memory at once.
If that's not possible (as you seem to indicate), then in your own method, you could write the String to a file as soon as you get it. (Assuming that the OutOfMemoryError doesn't occur before your own code starts.) Then read it back, one line at a time, and process each line as you get it. Writing and reading a file is probably slower than keeping everything in memory, but it avoids the OutOfMemoryError. It also may
not be slower, as it means garbage collection won't have to work as hard. Also the performance of writing and reading a local file may well be irrelevant compared to the database. The most important thing is to avoid the OutOfMemoryError. Fix that, then see if the performance is acceptable, and if not, identify where the slowness is really coming from.
Incidentally, CSV parsing can have a number of gotchas that are not initially obvious. It's usually simpler to use an existing library. Google "java csv parser" for a number of options.
In the code shown, you don't actually do anything with customInfo or phoneNos after you gather their data, and they become available for garbage collection every time you move to a new line. Is there more code inside the loop that you're not showing? You said: "Some of the fields(Max 5-8) in csv corresponds to same database fields, so before inserting them in DB I need to store them in a list or array." Does this refer to the ArrayList and HashMaps shown in the code here, or are you putting these records into
another big list? If you can send each record off to the database as you read it, rather than putting it in a big list of some sort, that will also help your memory usage quite a bit.