#1041 - Out of memory issue in mysql
PROBLEM #1
Your major problem is having at least 10000 tables
Here is the issue I see
RDS Instance was All InnoDB
How many file handles are open if you have 10000 InnoDB tables ?

One file handle for the .frm file
One file handle for the .ibd file

This would be a maximum of 20000 open file handles
RDS Instance was All MyISAM
How many file handles are open if you have 10000 MyISAM tables ?

One file handle for the .frm file
One file handle for the .MYD file
One file handle for the .MYI file

This would be a maximum of 30000 open file handles
PROBLEM #2
You are using m1.medium. That only has 3.75 GB RAM.
PROBLEM #3
Having 10000 tables can be very memory intensive because of the amount of metadata to maintain
See my old posts about INFORMATION_SCHEMA's memory consumption

Apr 22, 2014 : Do Inactive MySQL Databases Consume Memory?
Apr 21, 2014 : Adding new tables -- memory usage increases

PROBLEM #4
Your Production Server probably has too many open DB Connections that are dormant but consuming memory (See my post How costly is opening and closing of a DB connection?)
ANALYSIS
Your problem could simply be having too many open tables at the moment you are trying to create a table (which needs 2-3 file handles) or an alter table (which needs 2-3 file handles). I have seen this happen to me trying to create a partitioned table and running out of file handles. I wrote about this in my old post What are the possible risks involved in partitioning large database tables? where I raised the ULIMIT on the OS (bare metal server) to address it. I know changing ULIMIT does not help you because you are in RDS.
SUGGESTIONS
Simply run
mysql&gt; FLUSH TABLES;

and it will close all tables that have open files handles.
If you prefer to close specific open tables, you can list the open tables with
mysql&gt; SHOW OPEN TABLES FROM &lt;database&gt;;

Then, you must close the tables explicitly like this
mysql&gt; FLUSH TABLES db1.tb1,db2,tb2,db3.tb3;

After running FLUSH TABLES;, then you can run CREATE TABLE or ALTER TABLE.
You may also need upgrade to another server model with much more RAM.
You could reduce the number of tables but archiving the data and removing inactive databases. This will reduce RAM consumed for the INFORMATION_SCHEMA.
You should also close all your DB Connections that are not being pooled.
GIVE IT A TRY !!!