Is there any other option other than selenium grid?
To Answer your first question, "How to run tests in multiple browser parallel?", you can use TestNG framework for parallel execution.
I have developed a framework which will help you with parallel execution.
You will have to import given framework into your maven project or you can download JAR file and add it to your build path. Once done, you can extend BaseActions class, that will have all necessary declarations with protected access specified. You can use TestNG.xml file to do parallel execution,
Sample TestNG.xml: https://github.com/qamate/orangehrm-selenium-automation/blob/master/testng.xml
Hope that helps!