Is the husband's refusal to accompany his sick wife to the doctor, his delay in doing so, his forbidding her from going alone, as well as his refusal to respond to her request for intimacy and his shaming of her, considered a denial of conjugal rights?

The husband must be considerate of his wife, and each of them must bear the other's shortcomings and mistakes. A believer does not despise a believing woman; if he dislikes one characteristic, he will be pleased with another. There is no شرعي (Islamic legal) impediment to each spouse enjoying the other, and they have the right to observe that. It is customary for the initiative to come from the husband due to the prevalence of shyness among women. Try to convince your husband that there is no need to adhere to customs that have no شرعي (Islamic legal) basis. If you are unable to, then it is in both your interests for each party to be considerate of the other.