I lost my firstborn to medical error when she was 2 and a half. The first thing I said, as soon as I'd been told that horrible news, was that I wanted another child. Within a couple of weeks, I'd swung the other way and never wanted another, less because I didn't want an infant and more because I'd gotten to the point of recognizing that I wanted the baby I'd lost.
Feeling angry and cheated and heart sick is your right right now. Not just for yourself but also for your partner and precious boys. This is a loss that no words can ever thoroughly express and I am deeply saddened for your pain and trials.
This being said, I did indeed go on to deliberately have another child and am even pregnant with a third. My second dd came about a year and a half after her sister's death, when the grief of our first loss had dulled to a steady and familiar companion and left room for my real desires to be a mother to resurface. Between dd 1's passing and dd 2's conception I suffered a miscarriage and a close associate of mind put an unwanted child up for adoption. I felt mocked. Angry. Last year I suffered another miscarriage just as my Sil brought home her firstborn. Those first few weeks of holding and watching someone else's baby were excruciating. My Sil understood and let me set my pace with my niece, whom I adore. Point here, loss sucks and grief often feels irrational. It's not. The pain of child loss cuts deep enough to scar the soul. Take the time to heal. You'll feel when it's right for you to move forward.
Ultimately, I agree that a new baby fills the craving to hold and protect an innocent little one. However, I also know from experience that nothing speeds the healing of such a loss. It knows no time frames and is deeply personal to each individual. More so, even when you feel you are ready to have another child, you may also find increased anxiety levels about the pending arrival's health from the moment you're aware of their presence long past the point of your last loss. And you will likely still be blindsided by the heart wrenching ache for the angel you no longer hold at unpredictable intervals. In short, babies are wonderful. But only time and a good support system can help you with the healing here. May whatever power in the universe you invoke comfort and guide you through the pain. My deepest prayers and sympathy go out to you and yours.