|Feelings are emotions and sensations. "Burdened", rather than being a Feeling, is a judgment. It is a Thought that is being claimed by the speaker to be a Feeling. Further adding to the VRP drama is the causal, "by". The speaker is claiming Victim status saying that he/she has been "burdened by" the other person. As with other Victim-type statements, the speaker is simultaneously a Persecutor.
"Always" and "having to be" in the statement are additional examples of Victim -- Persecutor judgments. Speaking in the present tense here about past events implies "badness" about the other person with the assumption that he/she will operate that "bad" way in the future.
||The Green here is in the statement of an actual Feeling (frustrated) about the occasions that have happened previously (Observations in the past tense -- allowing room for possible future change).
A possible Want statement that might follow could be something such as: "I would like to sit down with you this evening and brainstorm different ways to trade-off her care if she were to get sick again.