The thing is I find this both comforting and scary
I really understand this. When I had not believed in God (for a lot of years), I felt like I was going to jump off a cliff if I let go of my unbelief and trusted in God instead of my own works.
I was first introduced to the idea that God may be real when I came across a well-known, but perhaps little understood, verse in the bible: John 3 verse 16 which says "for God so loved the world, that he gave His only son, so that whoever believes in Him should not perish but have eternal life".
I looked deeper into the context of the word "believe", and found it meant to trust in and rely upon HIM. Other verses in the bible spoke of how God says we can't earn our own way to Him through; good works, going to church, being baby baptised etc. and fitted well with this new concept: a free gift from God, that all of us at some point in our lives either chooses to accept or reject. A gift that is given freely because everyone has done wrong at some point in their life and there is no-one righteous enough, meaning perfect enough, to be above needing this gift.
I'm started to worry I will be punished for things I have done in the years before.
This is perfectly normal and the reason you feel this way is likely to be because you've realised, perhaps for the first time in your life, that you're what the bible calls a 'sinner'. I'm one too, we all are. It just means we do wrong and God's spirit it prompting you to know that you deserve punishment, just like we all do. The bible says "the wages of sin is death, but the free gift of God is eternal life". It really is good news to learn that Jesus paid the penalty so you don't have to. The bible says "He paid ONCE; for ALL". Anything you have done wrong in the past, or will do wrong in the future is covered. There is no need for worry when you see this, it brings instead a deep gratitude for such undeserved grace and mercy.
I worry I am not worthy and therefore haven't even been to church yet.
None of us are worthy of God in ourselves because none of us are righteous.
Philippians chapter 3 verse 9 says: "But not having a righteousness of my own...., but that which is through faith in Christ, the righteousness which comes from God on the basis of faith"
Romans 4 also says "Now to the one who works, his wage is not credited as a favor, but as what is due. But to the one who does not work, but believes in Him who justifies the ungodly, his faith is credited as righteousness, just as David also speaks of the blessing on the man to whom God credits righteousness apart from works
^“Blessed are those whose lawless deeds have been forgiven,
And whose sins have been covered.
“Blessed is the man whose sin the Lord will not take into account.”^
I knew I hadn't done anything hideously wrong by most people's standards, but I also knew that no one really is perfect and that included me. I now know I am made righteous by Jesus, because of my faith, and not of myself.
By all means find a good church where you can grow, but do test their teaching is not contrary to the bible, otherwise you're following a man-made religion instead, which is pointless. My recommendation to you is to research it all for yourself, take no one's word for it (either for or against), the answers are all there if you take time to read and study them out.
These worries were not there when I was an atheist so finding God has created a lot of questions in my mind.
Sometimes we don't let ourselves think too much, I know I didn't. But asking questions is a very good and healthy place to be, don't let anyone try to stop you! Even God says we should "test" and "search" teachings.