He wasn't 190 years old, nor was he physically 124 years old.

Physically, he wasn't 124 years old, but he was close. He was frozen in ice when he was 27 years old (he was born in 1918 and was frozen in 1945; 1945 - 1918 = 27). When he was unfrozen, it was 2011. Prior to going back in time to 1945 at the end of 'Avengers: Endgame', he was 39 years old (2023 - 2011 = 12; 27 + 12 = 39). When he went back in time to 1945 and was then seen again in 2023 after having stayed in the past, it had been 78 years, making him 117 years old (39 + 78 = 117).

Finding his total age is now easy after doing the math for his physical age. Since he was frozen in 1945 and unfrozen in 2011, he was frozen for 66 years, so that means that he was 137 years old (78 + 66 = 137).

tl:dr Total age is 137 years while physical age is 117 years.