My guess is that your headaches are coming more from your breathing. Since it appears that they are starting with your continuous swims (and not your other workouts), this would more likely point to your breathing while continuous swimming. Are you holding your breath? How often are you breathing? How are you breathing in? Breathing out? I would take a look at how your breathing might change when you go from interval training to continuous pool swims.
Does any of this resonate with you? While I goggles might play a factor, I don’t understand why they would start now versus not before. And the swim cap doesn’t get tighter with use. It actually gets looser. Thus I would look at how you are breathing and see if you can eliminate what you are doing/not doing (like holding your breath) between your regular pool swims and your continuous swims. Here’s hoping you can resolve it asap!