Yes, you can doubt your salvation. If this were not the case, 1 John 5:13 wouldn't have been written. I've been a Christian for decades but there was a period of time when I doubted. It about drove me nuts. I finally had to simply *decide* to believe. Either the Bible was trustworthy, or all bets were off. So I'm betting my life on the Bible, having decided that it is true, and that since I'm trusting in Jesus to save me He will.
This is the key. You have to decide to believe. If the blood Jesus shed was not enough to pay for your sins for all eternity, nothing ever will be. If and when you have moments or times of doubt, you have once again decide to believe that what God did for you on the cross is good enough to save you and nothing else ever was, and nothing else ever will be.
Romans 3:24-26.....Being justified freely by his grace through the redemption that is in Christ Jesus: Whom God hath set forth to be a propitiation through faith in his blood, to declare his righteousness for the remission of sins that are past, through the forbearance of God; 26To declare, I say, at this time his righteousness: that he might be just, and the justifier of him which believeth in Jesus.
It's through faith in His blood, what He did for us, He gave His life's blood as the payment for our sins and we our debt to God has been covered by His blood. This is the assurance we have, and we have to decide to believe it. When we fall into doubt or unbelief, if we have received Jesus Christ as our Savior, that doubt or unbelief is sin. The more you call that doubt and unbelief "sin" and repent of it and leave it behind by deciding to believe God and take Him at His Word and trust in what He did to save you from Hell, the less that doubt and unbelief will pop up in your thoughts and feelings to torment you with fears that you might really not be saved and might really be on your way to Hell.
We simply have to decide to believe God and take Him at His Word....quoting the above post from dysert: " Either the Bible was trustworthy, or all bets were off. So I'm betting my life on the Bible, having decided that it is true, and that since I'm trusting in Jesus to save me He will".
He not only will save you, He did save you. He will save anybody who will repent and believe on the Lord Jesus Christ. That is why we try to tell others about what God did for them so they can be saved.