Supercryptid, welcome to CU!
Don't allow the enemy to steal your joy and peace. If you have asked the Lord into your heart and placed your faith and trust in Him, you
are saved!
Rom 10:9 That if thou shalt confess with thy mouth the Lord Jesus, and shalt believe in thine heart that God hath raised him from the dead,
thou shalt be saved.
Grab hold of that verse and tuck it away friend!
I actually wrote a thread not too long ago called Blessed Assurance...somewhere in the Theology forum about this very thing.
There are some folks who may try to tell you all sorts of things like that. When the Holy Spirit takes up residence in your heart, you will notice a few things, which I believe is clear evidence of salvation. Feeling guilty about sinning!

I would say this is strong evidence of His presence in your life.
Rom 8:5 For those who are according to the flesh set their minds on the things of the flesh, but those who are according to the Spirit, the things of the Spirit.
Rom 8:6 For the mind set on the flesh is death, but the mind set on the Spirit is life and peace,
Rom 8:7 because the mind set on the flesh is hostile toward God;
for it does not subject itself to the law of God, for it is not even able to do so, Do you feel guilty when you sin? Do you humble yourself to Gods provision for that sin (Christ) asking His forgiveness? This IMO would be strong evidence of salvation, because it is subjecting ones self to the law of God. Christians are the only ones who know this struggle. Wanting to do what is right, and struggling with the flesh to overcome our sins. If you sense this battle going on in your life, God lives in your heart, no doubt about it!
You said:
I go to church because I know that I should do it, because the Bible says to, not because I feel drawn in some special way.
Bingo! The Holy Spirit will prod you to do right, even though we may not always want to

Rest in the assurance of Christ friend and continue to grow in your faith. Your walk is a process, but your salvation is a done deal...Paid in Full!
Grace and Peace!