OP: yes, it will (probably) get better. When? In our experience, ages 2-3 (especially 3) were the worst, and things started to calm down a bit starting somewhere during age 4. That's very typical. Depending on the kid, ages ~5-12 is probably the sweet spot, so in a couple years you'll hopefully have around 5 years of relative bliss until your older son hits his teens...and then it's a crapshoot.
One thing we've noticed is that when either of us (parents) are trying to accomplish anything -- especially "work" work, but including housework, sending an e-mail, etc. -- then the normal kid background noise that you describe becomes unbearable, just as you're experiencing. We become very irritable, and that's not good for anyone. So we've learned that if the work can wait, it's better to put it out of our minds and just focus on engaging with the kids.
But even when purposefully engaging with a good attitude, each of us can take only so much of entertaining young children, so we find that tag-team (taking turns), divide and conquer (1 kid per parent is so much easier than 2+), and outside help (sitters, daycare, camp) are the best strategies. We employ the first two frequently on weekends when all 3 kids are home.
Obviously if you're working from home, you can't just stop working all day to play with your kids. In this case the easiest solution would be to have your DH bring the kids outside, to the park, to the grocery store, on a field trip -- anywhere but in the house. :) Have a talk with him and let him know how hard the current arrangement is for you, and hopefully he'll be on board. There will be times when the kids will have to be at home -- around naptime or meals, etc. I suggest you invest in a good pair of sound isolating headphones to help you get through these times.
I'm not sure whether your DH is the full-time childcare giver while you work, or if you alternate days. But regardless, if the childcare burden feels like too much to take at times, Laura33's observation is spot on. There's nothing wrong with getting help when needed. If daycare/camp is out of the budget, you could try to find a sitter who can help out occasionally as needed. I bet even a few hours a day, a few days a week, would do a lot to relieve stress. Or during the summer maybe you could find a "mother's helper" (or father's helper!) -- a neighborhood pre-teen or young teen who is willing to play with the kids and help keep them entertained for very little $$.