you can check if your session has a row in V$TRANSACTION
(obviously that requires read privilege on this view):
SQL> SELECT COUNT(*)
FROM v$transaction t, v$session s, v$mystat m
WHERE t.ses_addr = s.saddr
AND s.sid = m.sid
AND ROWNUM = 1;
COUNT(*)
----------
0
SQL> insert into a values (1);
1 row inserted
SQL> SELECT COUNT(*)
FROM v$transaction t, v$session s, v$mystat m
WHERE t.ses_addr = s.saddr
AND s.sid = m.sid
AND ROWNUM = 1;
COUNT(*)
----------
1
SQL> commit;
Commit complete
SQL> SELECT COUNT(*)
FROM v$transaction t, v$session s, v$mystat m
WHERE t.ses_addr = s.saddr
AND s.sid = m.sid
AND ROWNUM = 1;
COUNT(*)
----------
0
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