Breastfeeding and pumping

Edited: I alternate sides. I don’t only use one side every time I just don’t do both at every feeding.

So when I breastfeed I always use one side and have my haakaa on the other side. Usually when I have to go somewhere and I know I’m not going to be able to nurse while I’m out I’ll pump so I can take a bottle. I’ve noticed though that when I do that, the breast that he last ate from seems to fill up a lot faster and get uncomfortable. I’m assuming it’s because it’s getting double stimulation? So my question is, when I do have to pump to go out, would it fix that problem if I just pumped the side he did not just eat from and just use the haakaa on the other one like I would if I were nursing?