Acts 2 definitely lines out that baptism is required to receive the forgiveness of sins.
You need to properly harmonize scripture with scripture before reaching your conclusion on doctrine. In Acts 2:38, "for the remission of sins" does not refer back to both clauses, "you all repent" and "each one of you be baptized," but refers only to the first. Peter is saying "repent unto the remission of your sins," the same as in Acts 3:19. The clause "each one of you be baptized" is parenthetical. This is exactly what Acts 3:19 teaches except that Peter omits the parenthesis.
*Also compare the fact that these Gentiles in Acts 10:45
received the gift of the Holy Spirit (compare with Acts 2:38 -
the gift of the Holy Spirit) and this was
BEFORE water baptism (Acts 10:47).
In Acts 10:43 we read
..whoever believes in Him receives remission of sins. Again, these Gentiles
received the gift of the Holy Spirit - Acts 10:45 -
when they believed on the Lord Jesus Christ - Acts 11:17 - (compare with Acts 16:31 -
Believe on the Lord Jesus Christ and you will be saved)
BEFORE water baptism - Acts 10:47. This is referred to as
repentance unto life - Acts 11:18.
*So the only logical conclusion
when properly harmonizing scripture with scripture is that faith in Jesus Christ "implied in genuine repentance" (rather than water baptism) brings the remission of sins and the gift of the Holy Spirit (Luke 24:47; Acts 2:38; 3:19; 5:31; 10:43-47; 11:17,18; 15:8,9; 16:31; 26:18). *Perfect Harmony*
Having to choose to believe is an action also. Jesus said, “ If you love me obey what I’ve taught”. We also see repeatedly throughout the Torah that the Jews were Gods people and that they believed in god yet many times those who lived unrighteously and disobeyed were destroyed. Their actions, not just their belief, determined what happened to them.
Simply believing "mental assent" in the existence of God no more saved the Jews than "mental assent" belief in God of demons. (James 2:19) Living unrighteously in continued disobedience is a manifestation of unbelief. (Hebrews 3:16-19) Though you already know all this, I want to remind you that the Lord at one time delivered his people out of Egypt, but later
destroyed those who did not believe. (Jude 1:5)
You’re belief in God does not save you anymore than your fruits of the spirit. We are all saved by grace and mercy and we are all saved when we hear our names called in the book of life. To be given that grace and mercy and resurrect to eternal life you must have belief and works.
Those who believe in/have faith in/trust in/reliance Jesus Christ for salvation receive eternal life. Works are the fruit, by product and demonstrative evidence of saving belief in Christ, but not the essence of belief and also not the means of obtaining salvation. All genuine believers are fruitful, yet not all are equally fruitful.
Works Righteousness is the belief you deserve heaven because you’re a good person despite knowing we all fall short. It’s not the same mad saying we must pursue righteousness and truth.
It sounds to me like you are trusting in works for salvation and NOT IN CHRIST ALONE.