I echo @Sofacouchboredom.
Your feelings are valid, you don’t feel safe and secure yet. He needs to prove to you that you are, and just saying it is not enough. The burden is on him to make you feel safe, not on you to stop worrying about it. The worrying will die down and eventually fade away as and when he shows you, by his actions and concern for you, that he is a safe partner to be with.
Again, as Sofa says, in the first few weeks after an affair, especially one that he did not think you would ever discover, he will continue to lie, minimise and say pretty much anything to try to save his ass. If he is committed to saving your marriage, as he sees what he has really done to everyone, this will stop, and he will see what he has to do, but in the early stages he is in panic-damage-limitation mode, and because he is so used to lying, he will lie, OP.
Affairs usually end very messily indeed and lying is a way to try to control the now out of control mess (of his own making) and the people caught up in it. If a quick lie now stops that spinning plate from falling whilst he runs to catch another, he’ll do it. Anything to stop them all crashing down to earth. If OW is now desperate she will have turned up the volume and pressure, and if he feels badly about how he has treated her, he will minimise and lie to her to, to try to ‘let her down gently’. Lie to you to stop you leaving him, lie to her to stop her getting angry and upset and possibly make it worse for him with youx
Cheats never have a plan for being discovered. Unless they want to be discovered, because they are using the affair as an excuse to end their marriage, they usually think they were never going to get caught and the idiots are absolutely blindsided when they actually do. The ensuing panic means knee-jerk crisis management, which is when costly lies are told and huge mistakes are made and trust further eroded, more damage done.
Protect yourself now, make sure you know that it truly is over with OW, no reconciliation can start until you know she is history and deleted/blocked. Make that your non-negotiable red line.
After that, he needs to give up his privacy for a while and be totally accountable for everything: his whereabouts and reasons to be there, his timings, access for you to every device he owns, (yes, I know he can still get round this, even if OP sees his phone, but an unwillingness to do so is a huge red flag so ask and see what his response is) full access to all financial statements, and a full, frank account of what happened, where, and how and when it ended. Set out your stall of what you need to feel better, exactly what your red lines are and what will happen if they are ever crossed, and stick to it and be prepared to follow it through, however scary that is.
The way out of the feelings you are experiencing are through his behaviour, his actions, his total acceptance of responsibility for the whole thing, his remorse (not guilt, guilt is about him feeling bad for what he did, remorse is him feeling bad for hurting you) and his continual ongoing efforts to be an open, honest man. If he can’t or won’t do this, OP, save yourself the misery and ask for a separation at the very least. There is no point even trying to reconcile if he makes this about himself, it’s his responsibility to make you feel safe, his responsibility for destroying your trust, his responsibility to help you heal from the terrible damage he has done to you.
Don’t blame yourself for still feeling ‘paranoid’ (you’re not paranoid, your brain is still in flight or flight mode because of the trauma of his betrayal. It’s a normal response and not a weakness or defect) it is a consequence of his wrong choices that you feel like this. The ball is therefore in his court to help you out, do not feel bad about yourself for having a normal human response to betrayal. His character defects caused your constant anxiety and hyper vigilance, not yours. Take care of yourself, I know those feelings and I’m so sorry xx💐