Hi Dmytro Chasovskyi,
Before you can successfully run multiple projects at once, you need to know your own strengths and weaknesses. I am a Web Developer myself but I'm stronger on the backend, have an eye for details and communicate well.
With this knowledge, when I have a web project, I break it down to UI/UX, Design, Frontend and Backend. Luckily, I have friends that are better and faster than I am in those areas so I outsource the work to them and pay them well too.
As you do this, you find that you can handle more projects than tackling the entire project alone each time. Form a strong team and delegate well.
If you don't have friends or colleagues like that, you can hire it out to experienced and skilled people.
As for tools, you can keep it simple by using Trello as HenryM suggested above. It's quite easy to learn and master if you don't already know how to use it.
Trello being a simple tool, if any of your team members don't know how to use it already, you can help them learn it quickly.
Tip: You can use also a color scheme / labels on Trello to track issues.