If you came from an area in Hungary in which tuberculosis (TB) was endemic, the positive skin test equally likely to be on the basis of administered Bacille Calmette-Guerin (BCG) vaccine, as on the basis of a prior TB infection, be it currently active or inactive infection. Maybe even more likely to be the latter, since the propensity to have a positive skin test in response to BCG, diminishes progressively over time and, in many BCG injected people, will revert to negative after 10 or more years have passed. It is reasonable for your employer to suspend your employment until the issue of TB infection is resolved. Bottom line is that you should not assume that the positive skin test was caused by the BCG.
If the skin test was weakly positive, it is unlikely that a repeat tuberculin skin test (TST) would cause a serious reaction, assuming that intermediate strength tuberculin was used. Another option is a serological test for TB called the QuantiFERON-gold in-tube test or The QFT-GIT. Some experts believe that the QFT-GIT shows the potential to replace the TST for latent TB infection (LTBI) screening in refugees from tuberculosis-endemic areas.
You definitely should have a chest x-ray, taking whatever actions are required to get one. If raising any sputum, it should be sent to the public health lab for staining and culture.
Good luck.