My question is if I have grounds to seek compensation for wrongful discharge and defamation?

Two female co-workers that I had relations with, contrived to get me fired, and HR not only allowed it, but appears to have facilitated it. Woman (A) filed a harassment complaint as a result of woman (B) mistaking a comment in one of our text conversations. And without clarification began to gossip and raise concern. I was placed on leave pending investigation. Just that morning I learned that these two had been in communication for over a month, yet woman(B) portrayed herself as my loyal friend, and I sought out advice from her for my dilemma with woman(A). When I was called back into work six days later for questioning, I was informed that woman (B) had placed a complaint against me as well. She claimed that I threaten to inform HR and her husband of our affair if she spoke to HR about Woman (A) and me. I told HR that was absurd, what was woman (B) going to be able to tell about woman (A) and I, that woman (A) would not have already told. Any of the information would have been second hand that she heard from woman (A). Not only that but why would I tell HR, they aren't going to do anything about her affair. And there was no reason from me to tell her husband, thereby ending any benefits. I was not aware at the time that woman (B) had hurt feeling and was very upset with me. HR is fully aware that these women both had the motivation get me in trouble. The two HR persons were female as well, and I don’t think they were very objective in their investigation. The finding appear as though woman (A) claims were dismissed because of the time that had passed. Woman (B) complaint was the cause for me to be terminated. There was nowhere that in any documentation that I submitted that has anything other than subjective text that doesn’t even mention her husband, nor the affair, and it doesn’t even have any supporting statement. Cause it simple did not happen. I talked to woman (B) a few weeks after I was fired, and not only did she admit to spreading gossip about me, she informed me of stuff that the department director was saying that I said. It was information that she would not have known from anybody other than him. Not that he is a very honest guy anyway, only weeks before he had offered to fix the times as to not reflect my late arrivals in exchange for me purchasing a discount card. And he had also bypassed the normal hiring process to give woman (B) her position. Never was the position posted, nor were interviews done. The other student that was doing clinical at the same time as woman(B) was not given the same chance, she was more qualified but perhaps her being a person of size played a role in the Director promising woman(B) the position six months in advance. Which was also odd because she did not have the proper credentials, and on file it was a different person.
So my discharge was reported to Group One and will forever affect my future earning, I will not be eligible for rehire with this organization or its affiliates, which covers a huge portion of the market, even the department Director and taken part in dragging my name through the mud, and I had another employee call me up with accusation that were not true, and threats. He would never have even thought it was me, if he hadn’t heard about the harassment complaints.
I have worked there for several years without anything negative actions or events in my file. I had the highest production numbers. And always went the extra mile. The allegations against me are either not true or grossly exaggerated and I certainly don’t feel that termination was fair. I gave information repeatedly that support my claims, I my claims didn’t leave all the unanswered questions like theirs did. I gave more than adequate proof that this women's actions were premeditated, motivated, carried out with the intent to cause harm, and that they had history of previous deceit and betrayal. I believe I was terminated in an attempt to cover up the embarrassing fact that the poorly executed investigation was done with bias and without diligence causing a loss for me. It is in the fact the the reason for my termination occurred after I was put on leave.
I have been through the internal review process, and my request for reinstatement was denied. I am obligated to have a hearing by arbitration rather that by jury. Do I still have good cause to seek compensation? They ruined my life. And all I wanted to do was just go back to work.