In response to the question:
If you start java multiple times, multiple copies of java will be running with each their own memory. Eclipse and websphere are probably started separately so use independent memory. Your trouble should not be there.
In response to your problem
Out of Memory
Both Eclipse and Websphere can gobble up memory like there's not tomorrow. Look al the -X flags, the flag for perm gen space should be added to the flag for heap space to get the memory consumption. Also allow some overhead for the OS, windowing environment, e-mail client, browser (500 MB - 1 GB or so, depending on the OS and what you're running). So it can be that the computer is out of memory.
More frequently the amount of memory assigned to the jvm is just not enough. Java has not been started with enough memory for the app assigned to it. It's up to you to deduce if it is Heap Space which ran out, or PermGen space. Both can be adjusted, have a look at this website. The flags are -Xmx and -XX:MaxPermSize. Look at the start scripts for Websphere, as that's the one complaining.
Recommendation
Check which kind of memory is out, and search for that on stack overflow; either PermGen or Heap Space should do.