There used to be hippos and other such rainforesty creatures in the Sahara, that's true. Those parts were once pretty green and wet. But that was during the ice ages, when all climatic bands were compressed towards the equator. As soon as the heat went on at the end of the last ice age (about 10,000 years ago), the climatic bands started shifting towards the poles. turning the green haven the Sahara was into the scorching desert of today. There are fossil records of hippopotami in the Sahara no older than 8,000 years. These conditions also explain why there's so many animals living in both the African rainforest and the jungles of India, while there's no climatic connection between the two: there used to be, until the ice age pushed the desert between 'em.
As a matter of fact, most moisture in a rainforest is generated by the forest itself. It evaporates, rains down, evaporates again etc. Of course it initially got its moisture because of its proximity to an ocean, but if you give it long enough, even the hypothetical Sahara-on-the-equator would eventually be 'colonized' by a rainforest, since it conveniently carries its own water supply with it. Best example of this is the Amazon Forest. While only being climatically connected to an ocean on the east, even the westernmost stretches of the South American plains are covered in lush forests. Take for example the Peruvian rainforest, which gets its moisture from the Atlantic Ocean (about 1700 miles away) and not from the far closer Pacific (about 200 miles tops), which does not induce any rainfall in the Amazon due to the fact that there's this insurpassable wall, the Andes Mountain Range, blocking all westerly winds.
Another example? Take the African Rain forest, 3300 miles on its longest (reaching from the coast of Senegal to the Congo-Uganda border). The easternmost stretch hugs the mountain ranges of the Great Rift Valley, and is more than 1500 miles away from the ocean that feeds it. If these mountain ranges hadn't been there, it'd have marched all the way to the Indian Ocean, where the conditions for rainforest formation are just as good. The GRV works in both directions by the way: there's another rainforest on the other side of the ridge as well, stretching through northern Kenya all the way to the coast.
Basically, as long as there's no mountain ranges blocking its path, a rainforest will just keep creeping on. (But only within that 'rainforest friendly' band around the equator of course)
EDIT:
This might be important for your map: deserts might form on the equator if they're completely shut off from any ocean. Take for example the Nyiri Desert in southern Kenya. So if a desert on the equator is what you're after, just put some walls around the spot .