What helped me to trust the pill (when I was on it) was understanding how it works. If you're taking your pill correctly and are accounting for vomiting, diarrhea, or absorption inhibitors like certain medications, you only have a 0.3% chance of pregnancy on the combination pill. The 0.3% chance is pretty statistically insignificant. It's basically because NO medication or medical procedure can ever be marketed as being 100% effective because there will always be at least one person it doesn't work for. And when that happens (which is almost never) its usually because they have some other medical condition going on. Even sterilization isn't considered 100% effective. No drug company will ever market ANYTHING as being 100% effective. And when people say they got pregnant on the pill it's almost always because they weren't taking it properly. Be it they had vomiting or diarrhea they didn't account for, missing pills, or even being prescribed or taking a medication that inhibits absorption of the pill. And many people forget that sperm can survive for a couple days, so they may have had sex a couple days ago, missed 2 pills, and then think the sex was so long after that it wasn't an issue. When people say they get pregnant on the pill, it is almost always because of user error, but they often don't want to admit to it. Even if someone says they were a perfect user, that can't be relied on as we aren't sitting there with them all day watching them take the pill and not miss any (be it due to not taking it or things like vomiting and diarrhea).
The combined pill gives you 3 lines of defense:
1. It prevents ovulation so that there is no egg present to be fertilized 2. It thickens the cervical mucus so that sperm can not reach the egg to fertilize it (in the extremely unlikely event that an egg is even released-- which does not happen if you take your pill correctly), and 3. It thins the uterine lining to the point where even if the first two lines of defense failed (which wouldn't happen) and an egg was released and successfully fertilized, it cannot attach to the wall of the uterus. And all that is much more effective than condoms, it's basically like using 3 extremely effective methods of birth control. Condoms can be comforting mentally because you have an actual physical barrier between you and the sperm, but the fact is they just aren't as effective as hormonal contraception. And if you're on hormonal contraception and using it properly adding a condom to that only increases your protection rate by like 0.01%, which is pretty statistically insignificant.
All that being said, if you aren't comfortable with having condomless sex, then don't. It's not worth being a nervous wreck and not enjoying sex because you're so worried about the extremely slim possibility of pregnancy. Nobody can tell you when you're ready to only rely on the pill, or even if you ever will be, that's totally up to you and what you're comfortable with.
And on top of that, condomless sex is only advisable if you're in a monogamous relationship and have both been tested for STIs and have been given the all clear. So if you plan to engage in condomless sex make sure you both get tested for STIs! Both a blood test and urine test.