I'm so sorry that you're suffering from this very frustrating problem and that the strategies you've tried so far have not helped to resolve your situation. I'm not surprised that you feel so desperate but well done for persevering so far.
I see that you already tried several good strategies but I wonder whether anybody has considered that the problem may be with your baby. Often, problems with feeding only on one side are related to the mechanical removal of milk by your baby. Sometimes, babies heads are tilted slightly to one side favourably. This is often related to a condition known as torticollis, where the muscle on one side of the neck is slightly tighter causing the baby discomfort turning ahead. Classically this causes problems with feeding on one side only either with the baby refusing to feed on that side or with repeated problems such as mastitis, blocked ducts, low supply, or pain.
Torticollis off and also causes flat head syndrome although in the early days this is usually very mild and subtle and therefore difficult to spot, which may be why nobody has picked up on it so far. It is thought that at least 30% of babies have some degree of torticollis and/or flat head, and it can be caused either in utero, during a long, difficult or instrumental delivery, or gradually occurring after birth as a result of a baby's preference for looking towards the light, or being held only on one side for example.
If you think this may be possible then the feeding problems are in fact a symptom of something that could potentially be treated with very gentle osteopathic or physiotherapy techniques so I urge you to see whether this may be your underlying problem. One way is to look at your baby from above and see whether there is any asymmetry in your babies head, or hold your baby in front of the mirror as often the change in perspective helps us to see something which we wouldn't normally see. You could also try placing your baby on their back on a changing mat and rolling them very gently 1st to one side and then to the other to see whether there is any stiffness or head lag on one side.
To get back to your original question, of course you can express only on one side as an interim or permanent solution to this problem. You would need to pump approximately as often as your baby would be feeding on that side. Be aware that your milk supply does not actually change between 1 to 6 months, i.e. a one month old baby drinks approximately the same amount of milk over 24 hours as a six month old baby, so do not be alarmed if your milk supply does not increase as your baby gets older and bigger.
To pump effectively, I suggest you watch this video, which will really help you to empty the breast as fully as possible, as a pump is not a perfect substitute for an effectively feeding baby: https://med.stanford.edu/newborns/professional-education/breastfeeding/maximizing-milk-production.html
I hope that answers your question, and more to the point, I hope you find a way through this situation that enables both you and your baby to enjoy feeding again.