Kind of.

The county of Barcelona was established in 801 as a subject to the Carolingian empire. In 878 the last Carolingian-appointed count was installed who turned it into a hereditary, autonomous post. He also strengthened the position of Barcelona, bringing new territories into its fold (like Girona and Osona which became core territories of the Barcelona counts).

Barcelona further distanced itself from the Carolings in the 10th century. In 985 it was attacked by Muslims and received no help from the empire. When the Caroling dynasty came to its end in 988 and the Capetian dynasty was installed, Barcelona allegedly didn't answer to the Capetian call to swear allegiance to the new Frankish king at which point the Counts of Barcelona would've become de facto independent. At this time the Count was Borrell II.

The subsequent counts (Ramon Berenguer I, Ramon Berenguer II, Berenguer Ramon II, Ramon Berenguer III (who brought the county of Provence into the realm via marriage)) further expanded Barcelona's power. Ramon Berenguer IV married Queen Petronilla of Aragon, ruling as King-Consort of Aragon. Their son Alfonso II inherited both of his parents' domains, creating the Crown of Aragon which is what people generally refer to when they say "Aragon".

The Kingdom of Aragon was also originally a Carolingian feudal county. It became a part of the Pamplona (Navarra) kingdom in the first half of the 9th century and the counts of Aragon died out, thus the Navarrese ruling dynasty got the lands. When King Sancho III died in 1035 his lands were divided, leaving Garcia Sanchez III as king of Navarra. Sancho III's illegitimate son Ramiro received Aragon and later Sobrarbe and Ribagorza when Sancho's son Gonzalo died. Ramiro fought against his brother Garcia Sanchez III to achieve independence from Navarra and Ramiro's son Sancho Ramirez ended up inheriting Navarra but the two realms were split again when King Alfonso died in 1135 without offspring. 15 years later Aragon formed a dynastic union with Barcelona.

Regarding the Spanish region, Valencia was later added to the Crown of Aragon via conquest of Muslim lands (the christian kingdoms in Iberia formed a pact for combating the muslims and pre-determined their desired territories between each other), and the Kingdom of Majorca, containing the Baleares and some mainland holdings in southern France, came to be a part of the Crown via dynastic machinations. Other regions, such as Sicily and Sardinia, came to be a part of the Crown even later but were rather an economic possession than a political one and not a part of the Iberian region so I won't go into full detail.

The reason why the Crown of Aragon would rather create new Kingdoms in acquired territories than expand the existing Kingdom of Aragon or county of Barcelona is the struggle for power between the King and the nobles, but I don't dare to touch that subject.