Jep - "EAG Pulse" doesn't sound like a ship name in ED to me. "Pulse" is a family of paintjobs - and there are Pulse paintjobs for the Eagle, so it might be that.
In the case you bought paintjobs: You need to go into outfitting (while in the ship type you bought the paintjob for) and then can apply the (non-functinal, btw.) paintjob to the ship. You don't buy ships for real world money in ED - you can't buy ships for real-world money in ED. You need to buy ships from a shipyard in the game, for in-game credits (which you also can't buy for real-world money, you 'll have to earn them by playing the game). Same goes for modules to outfit these ships, by the way.
Good news: the Eagle is a basically cheap low-tier ship (ok, despite its initial price of 43 kCr., you can spend a few MCr. on one if you want...) that should be available nearly on every shipyard. The Asp X is slightly more elusive and expensive, but you still can earn the Credits (plus rebuy, plus some better modules) within a couple of hours in-game. Of course, going fully engineered and adding the 5A V1 FSD will take somewhat more time to collect all the mats.