Hello Dave, Well, both seem correct but I would rather say "tomorrow I will have an exam” just because you didn’t plan it, so you probably have to do the exam, you didn’t plan it personally and freely. So, “going to” means you have planed something, and “will” is just something that will happen but you didn’t plan it. (It is just my opinion, hope it helps you).

They are both grammatically correct, but it would be unusual to use 'will' in this way in everyday conversation. In everyday conversation, the 'will' future - almost always contracted to 'll - is generally used when we are making new decisions and promises. For example: "I don't understand this exercise". "Don't worry. I'll explain it to you". "What do you want to drink? We've got beer, wine and lemonade." "I'll have a beer, please". "Does anyone want to go to beach with me?" "Sure. I'll go!" "Don't tell anyone I told you about this" "No problem. I'll keep it a secret!" Can you see that these are all new decisions that you've just made? Those are typical uses of the 'will' future in conversation. We don't usually use 'will' for plans and schedules or for things that have already been arranged. This is why it would be unnatural to say "Tomorrow, I will have an exam". It isn't wrong, but it sounds strangely formal and stilted. When we are talking about arrangements that have already been made, we use either the 'going to' future or a present tense: I'm going to have an exam tomorrow. I have an exam tomorrow. = to refer to a fixed schedule I hope that helps.

They are both future tense."will" you don't exactly know when you are will do something."going to"you exactly know what are you going to do.And yes both sentences are correct, but "I'm going" better

Personally, neither! Both seem unnatural to me. I'd say (and what I hear from native speakers): "Tomorrow, I'm having an exam", the present continuous. Hope it helps!