Carroll's time at Upton Park has been blighted by inconsistent form and a knee injury that kept him out of the Hammers' starting line-up for two months.
But Carroll did not struggle one bit on his return to the first-team on Saturday, bullying the Swansea back line before heading home the winner with 13 minutes left.
The 24-year-old, who is on loan at West Ham from Liverpool until the end of the season, was left out of England's squad to face Brazil next week, but his manager thinks the striker will be under consideration for the Three Lions' double-header against San Marino and Montenegro in March if his form continues to improve.
"He should (get back in)," the West Ham manager said. "As long as he can stay fit between now and the end of the season, get as many games as he can (he will).
"There is a lot more to come from Andy. If he produces better performances than he has today, and if he builds his goal tally up, finishes the season on a high, it will be great for us and it will be great for him."
Swansea's defeat means their seven-match unbeaten run has come to an end, but manager Michael Laudrup was not too downhearted about the outcome.
"We dominated quite well in the first half," the Dane said.
"They gave us more or less what we expected. We had the ball more, but they played direct and we know how good Carroll is in the air. Inside the box he's very dangerous.
"We could have won 1-0 or it could have been 1-1. After they scored we came back, had a few chances to equalise, but we just have to accept it."