Hard to tell anything without the results of what your program is spitting out.
What happens when you use NextKey? Give exact examples.
// test 1 (WORKING) returns correct public key and BTC address for 0x01 and 0x02 private keys
privateKey.SetBase16((char*)"0000000000000000000000000000000000000000000000000000000000000001");
point = secp->ComputePublicKey(&privateKey);
std::cout << " (" << secp->GetPublicKeyHex(true, point) << ") [" << secp->GetAddress(P2PKH, true, point) << "]" << std::endl;
privateKey.AddOne();
point = secp->ComputePublicKey(&privateKey);
std::cout << " (" << secp->GetPublicKeyHex(true, point) << ") [" << secp->GetAddress(P2PKH, true, point) << "]" << std::endl;
// test 2 (NOT WORKING) returns correct public key and BTC address for 0x01 private key only
privateKey.SetBase16((char*)"0000000000000000000000000000000000000000000000000000000000000001");
point = secp->ComputePublicKey(&privateKey);
std::cout << " (" << secp->GetPublicKeyHex(true, point) << ") [" << secp->GetAddress(P2PKH, true, point) << "]" << std::endl;
point = secp->NextKey(point);
std::cout << " (" << secp->GetPublicKeyHex(true, point) << ") [" << secp->GetAddress(P2PKH, true, point) << "]" << std::endl;
// test 3 as arulbero suggested (NOT WORKING) returns correct public key and BTC address for 0x01 private key only
privateKey.SetBase16((char*)"0000000000000000000000000000000000000000000000000000000000000001");
Point P(secp->ComputePublicKey(&privateKey));
std::cout << " (" << secp->GetPublicKeyHex(true, secp->ComputePublicKey(&privateKey)) << ") [" << secp->GetAddress(P2PKH, true, secp->ComputePublicKey(&privateKey)) << "]" << std::endl;
P = secp->NextKey(P);
std::cout << " (" << secp->GetPublicKeyHex(true, P) << ") [" << secp->GetAddress(P2PKH, true, P) << "]" << std::endl;