There are various ways through which you can check whether your email marketing campaign is actually working or not. One way is through checking the open rate of your emails, this metric suggests how many subscribers have opened your mail.
A higher open rate indicates your email campaigns are relevant and compelling. Another method is through checking the click-through rate (CTR) which refers to how many people have clicked the link you provided in the email content. Another way is by checking the conversation rate and comparing your return on investment.