Based on what you are saying, you cannot mention the medical reason since you cannot show hundreds of thousands of dollars of financial support. The only option is the tourist visa.
Not trying to discourage you but want to let you know how difficult it is to get a tourist visa. Last time I went to the US embassy in KTM for H1 visa, a lady next to me was so proudly telling me that she works for NGO and earns more than RS 3 lakhs a month in Nepal and she was applying for a tourist visa just to visit New York for a week. She showed me her credentials and paperworks and she was definitely earning 3 lakhs a month. After I my h1 visa was approved, i waited outside for that girl and asked her when she came out. She told me the visa officer told her he did not see any reason for her to visit NY and denied the visa.

However, you can give it a try. Tell your cousins to provide you an invitation letter. From your side you need letter from your UAE employer stating the vacation you have been given and you annual income. You will need any property valuation you have in Nepal, any family relations certification which will show you tie back to Nepal. You need to show your hotel booking and airline booking for the time you mention. Then you need to show sufficient financial support (bank balance, income) during your stay in US. Good luck, but i will be really surprised if you get the visa.

Not sure how much you earn, but let me ask you one question which visa officer will definitely ask you, "What will stop you from living and working in US illegally and not returning back once you arrive in US?".