Is it urgent that your son potty-train for schooling reasons? If not, just wait until your new baby is older. When your baby is on a better routine (4-hour cycles and then two naps a day), your child will be more willing to go on a routine.
My child was 29 months old when her twin sisters were born, and it wasn't until the twins were 7 months old that life was manageable enough for us to begin potty training. That same month my older daughter turned 3. She trained gradually over 3 months.
We used a blank calendar to mark successes, and she got "coupons" (vouchers) for candy or a movie time for successes with BMs and wetting in the potty. Expect only BMs at first, and then reward wetting in the potty as it happens. For every five successess (then 10, then 20, then a whole week clean), we would give a coupon for a toy from the dollar store, which was quickly paid for by the diapers we were not using! We also gave her a book of stickers from which she could choose one each time she was successful; we put a blank piece of construction paper next to her calendar. All of this was on a large poster, which had large pockets to hold the special "coupons." Finally, we would give her a "big-girl panty" coupon for each dry week. When she had seven, she left thick panties and went to regular thin panties.
This whole reward system was launched by having "Mommy time" for the project of making the poster and pockets. When there's a new baby in the house, the older child craves Mommy time for projects. Another benefit to using "coupons" is that the earned reward could be saved until the proper time: A child who is preparing for bed should not be immediately allowed to watch a movie or eat candy. These coupons could be redeemed the next day. This actually is like getting two rewards, because you have the coupon as a reward, then the redemption of it on another day as a second reward. What's more, the kid who wants multiple movies or sweets in a day can be given obvious limits. By the way, you have to keep raising the bar on coupon rewards, or the kid will earn more treats than you're willing to give.
Three years of age is not too old to start potty training. A few more months of adjustment with a new baby would be worth the wait. Good luck!