Any Mass you attend on August 15th, at any time during the day, would meet your obligation.
So yes, this morning your obligation would have been met and there would be no need to go to Mass again this evening.
Often evening Masses on Holy Days of Obligation are there for the convenience of those who work during the day and would not otherwise be able to attend Mass, but it is not necessary to go to that particular Mass. Any Mass during the day would satisfy your obligation, even if it were a funeral Mass (and thus not with the readings for the Assumption).
If you did want to go again in the evening you would be able to receive communion. You may receive a second time during the day as long as the second time is within the context of a Mass.