Is the wealth I get from this work haram? I repented to Allah sincerely and asked Him to bless my wealth. I pay sadaqah every month from my salary.
There is no doubt that paying a bribe in order to get a job is haraam both for the one who pays the bribe and the one who accepts it, and for the one who mediates between them. No exception is made except in cases where the bribe is paid to remove injustice or to attain rights which can only be attained through bribery. In that case it is permissible for the one who gives it but it is haraam for the one who takes it.
See the answer to question no. 25758.
So long as the job is based on a test for applicants, bribery is haraam in this case, because you were no better than anyone else and you have no particular right which you had to pay a bribe to attain.
There is a warning concerning bribery which should scare any wise person away from engaging in it. It was narrated that Abu Hurayrah (may Allaah be pleased with him) said: The Messenger of Allaah (peace and blessings of Allaah be upon him) cursed the one who offers a bribe and the one who takes it.
Narrated by Abu Dawood (3580), al-Tirmidhi (13360 and Ibn Majaah (2313); classed as saheeh by al-Albaani in Saheeh Abi Dawood.
If you have repented to Allaah and you give some money in charity, as you say, then there is nothing wrong with you remaining in this post, so long as you are qualified to work in it, because appointing someone who is not qualified is a betrayal of trust, the harmful effects of which are obvious to all.
And Allaah knows best.