What should I do?

I've been dating this guy for the past two months and I somehow found out that he lied about his profession, I had asked him to send some pictures showing around his work as he said he'd be quite busy that day so he sent me 3 pictures and i found that picture way to pixelated considering the phone he uses, didn't thought much into it days went by I saw he had edited his pfp ( mind you it was badly edited, a kid would differentiate ) with the background of the area he claims he works at, I confronted him about that he gave an excuse as he was too shy too ask someone to click pictures of him and he needed one professional image, later when I searched up for that background I found the previous images sent by him on that website and they were years old, I confronted about that too, he said he was getting frustrated as how I kept continuously ask for pictures and he was busy so he sent the ones he found on that website, I told him you had the time to download them for google but not the time to click one? He later said he could show his I'd and was sorry for what he did, he did showed me his I'd but there wasn't any much information to take out and let this thing go. Since then I've been continuously doubting his actions and he ain't doing anything to assure me.

I asked him multiple times that he can share if there is something you can tell, my love for you won't change and it now later things have lead upto some heated arguments, the feelings I had for him now I'm forcefully suppressing them not knowing what to do.

These are the few texts I exchanged with him -

why won't you do anything, why aren't you saving this, it's not always about what I want and not always what you say you want, you are clearly aware why we ended up like this and it was all your fault

i deserve an explanation, i deserve a way out of it, i deserve the assurance that what you told me was all true.

Its just not gonna solve on its own if you think by giving me time or not talking to me, it's just gonna make it worse, it's gonna be the reason why we won't work it out, seeing you disappearing slowly day by day makes me feel like maybe I was the one who ended up loving you, really how easy it's for you?

how can I trust you again, when in the first place you aren't even saying anything or showing any action?

His reply :

I told you I miss you every day and I mean every word of it. So far I've done nothing but try to make you feel safe, loved and cared for whenever we were together.

Time and again I've shown you that you can be comfortable with me and I would respect all of your autonomy. I made a mistake with what I did and I'm truly sorry for it, perhaps more than you'll ever realise.

I am in love with you. I do really want you in my life long term. I understand that your trust in me is broken now so I am sorry for it once more. However, as long as I live, I'll support you whenever you need me to because of the love I have for you.