A new game can take up a lot of time and focus for many people, so if you're like that, then waiting so you can focus on your exams while you need to is probably a good idea. The game will be here when you're ready for it, whether that's now or in a couple months.

If you choose to continue now, you can prepare your current character(s) for heavensward by continuing through the main scenario. The expansion's main scenario and at least the major new areas are going to require completion of the main scenario that already exists. If you wait and start when Heavesward is available, you'll be able to make an Au Ra character to do that content with. Both are good options.

As for whether you'll feel behind, that's what you should want in an MMO. The only time you're not "behind" is when you've run out of things to do, and you never want to reach that point. Being behind just means you still have plenty of gaming ahead of you, making the game worth sticking around for.

SE is quite careful to make sure that older content (especially content that's in the main story line) remains important, so you shouldn't have any trouble coming in later to it. Besides, there are likely to be a lot of new players, as well as players starting new characters, when the expansion comes and a new race is available, so you'd have plenty of company in being new to it.