Is there an etymological connection between 只得 (zhǐdé) = "be obliged to" and 得 (děi) = "to have to"?
The pronounciation of "得 (děi)" is not a formal usuage, which is from a dialect. 

"只得 (zhǐdé)" has two kinds of meanings in this pronouciation. 
1, Meaning "only have": "我只得这么一个弟弟” - “I only have this one little brother”; 
2, Meaning similar as "不得不” (have to), usually connect with a Verb, and indicating there is limitaiton from objective circumstance. While "只得 (zhǐdé)" usually follow by actions out of personal choice / decision,  "不得不” usually follow by actions with no choice.
e.g. "由于下雨，我只得取消徒步计划” - “I have to cancel my hiking plan since it is raining” (I can still go out for hiking but I decided not to)