I don't have any experience with lymphedema or anything similar, but I spend a fair amount of time studying the poses. I do have one student who has had a single mastectomy, but doesn't have lymphedema, and I work with her to get a stretch into her arm pit on that side - it's super tight.

So this is my advice from a pose view, for a person with tight arm pits and shoulders, but not with lymphedema - you'll have to wait for your oncologist for that:

It will not hurt you to bend your arms in down dog - in fact there's a version with your elbows on the floor - but I assume your arms are bent to the sides to take some of the stretch out of your arm pits? This is great to work the triceps and muscles around the shoulderblades - so no worries there.

For poses with the arms overhead, warrior 1, tree, etc. - I would take the arms wider - so rather than have the arms in-line with your shoulders, have them more out like a "V" - you can do this is dog pose as well, but it can run into issues when you flow from one pose to the next. If that doesn't work, just bend the elbows.

Many yogis consider inversions good for the lymphatic system. You may also want to ask your doctor what he/she thinks.

Best of luck