How can I avoid making my toddler feel bad while I am breastfeeding my newborn?

Make him take part. By including your toddler during breastfeeding, he/she can become part of the team. Your toddler can hold your baby's hand, hand you the burp towel and even help pat your little one during the burping process. Praise and positive words will bring a smile as well.
Get him/her involved. For toddlers, time=love so if you spend extra time feeding baby you must love them more. This also involves changing & bathing. They see you smiling so they don't see it as work. I have had success breaking that idea by making todler first assistant for all feeds, changing, etc. Get them a bag to carry and have them bring diapers, burp wrag etc. After a brief period they get bored & stop hovering.