To be under anything means to be bearing the weight of that thing. The Good News that there is therefore now no condemnation has lifted the weight of the law off our backs.
You may argue that we are still subject to the Law; and in a sense that I will comment on later that may be true.
I am also subject to Jesus, my Lord; but He is not standing on my neck.
Eph 2:10 and Jas 2:14-18 indicate that works of righteousness will indeed follow Salvation. The point of disagreement is 'Whose works?'. You think you get credit for your obedience (if it is real). I think that the Holy Spirit within me gives God credit for my obedience.
Regarding being subject to the Law:
Since we (believers) are in Christ: 2 Co 5:15-21
15 And that he died for all, that they which live should not henceforth live unto themselves, but unto him which died for them, and rose again.
16 Wherefore henceforth know we no man after the flesh: yea, though we have known Christ after the flesh, yet now henceforth know we him no more.
17 Therefore if any man be in Christ, he is a new creature: old things are passed away; behold, all things are become new.
18 And all things are of God, who hath reconciled us to himself by Jesus Christ, and hath given to us the ministry of reconciliation;
19 To wit, that God was in Christ, reconciling the world unto himself, not imputing their trespasses unto them; and hath committed unto us the word of reconciliation.
20 Now then we are ambassadors for Christ, as though God did beseech you by us: we pray you in Christ's stead, be ye reconciled to God.
21 For he hath made him to be sin for us, who knew no sin; that we might be made the righteousness of God in him.
KJV
and He is in us: Col 1:25-27
25 Whereof I am made a minister, according to the dispensation of God which is given to me for you, to fulfil the word of God;
26 Even the mystery which hath been hid from ages and from generations, but now is made manifest to his saints:
27 To whom God would make known what is the riches of the glory of this mystery among the Gentiles; which is Christ in you, the hope of glory:
KJV
we are indeed subject to the moral principles of the Law but not to its penalty. Christ in us has fulfilled the Law on our behalf; and we in Him obey the Law but not of ourselves or to our credit. The Holy Spirit within us provokes and enables us to do His good pleasure.