Company Fires Me After They Convince Me To Stay

Company fires me after they convince me to stay when I was leaving.

So I worked in a small company in VA with some people from my home country. The work was too much but it had its benefits. I was treated fairly and given leave on short notice when something urgent happened. I found a job somewhere else with better pay and wanted to leave when my boss negotiated with me and convinced me to stay. When I decided to stay and work for them. The way they treated me changed. I suddenly was given more and more work and had to stay late mostly. A new employee joined us as well and I was told to train him. I did my best to train him because the management said they wanted to reduce my responsibilities since I had too much to do. After a month of training the guy I called in sick one day and got an email stating that I was terminated for not being punctual. No notice or warning was given to me and they mentioned verbal warnings in the email but they never gave me any. I was caught by surprise and got very upset I just emailed them and said I wasn’t given any notices or anything I tried telling them that why did you guys changed your treatment so fast and made me work more hours only to fire me for not coming because I was sick. I got an email back which said if there was a change in the treatment you should’ve told management and stop these accusations of not treating employees fairly otherwise we will take legal action. I am confused can they just do this and fire someone without a reason and then threaten me with legal consequences when I ask them for the change in attitude? I am worried about my record with other companies how can I apply to other companies when I am fired from a position with such accusations. They clearly just ruined my record. Any advices please ?