Short answer: Enjoy them! Really feeling your feelings is the best reminder of how beautifully intense life can be.
Long Answer: We’ve all been in pigeon pose, or a deep backbend. and suddenly wanted to cry (am I right?). Undoing physical tensions and blockages, some of which have been in place for years and decades, will often manifest as a sense of relief, a wash of freedom, or an intense emotion. Sometimes you’ll have memories float up, and sometimes the feelings will be inexplicable. No worries— there are two ways to go forward.
You can re-bottle your feelings! Push them down and away, pretend they don’t exist, ignore them, tell yourself you’ll deal with it later, or (my favorite) intellectualize and then forget about them.
This method is the quickest, least effective fix. The results is that we end up facing the same tensions and feelings again and again, or avoiding certain parts of the body, certain postures, so that we can more effectively avoid the feelings within us.
Unfortunately, avoiding the tensions don’t release them. Until we process and release the emotions, we carry them around in our body, like literal emotional baggage. Sometimes they (the emotional pattern as well as the physical pattern) manifest as our personality, and part of the difficulty of releasing the old tensions is that we have unconsciously taken them on as our identity.