Yes, you can pray Eid at home. Although it is not as common as praying in the mosque, there are many people who choose to do so for a variety of reasons. Some may not be able to make it to the mosque due to health or work commitments, while others may simply prefer the peace and quiet of their own homes.
There is no wrong way to pray Eid. As long as you are sincere in your intentions and focus on seeking Allah's forgiveness and blessings, He will accept your prayer regardless of where you are. If you are unsure of how to perform the prayers, there are plenty of resources available online or from your local mosque that can help guide you.