WA state employment law, employee's rights to get accumulated sick leave transferred to new company via merger

Employer and medical coverage: I am in Washington State. The company I work for was bought out by another company. This new company did not transfer over any of my 300 hours of accumulated sick time. Under this new company, I went to see a doctor; after which, the doctor wrote a note for me to take 3 days off from work - during treatment. My employer says I have no sick time and that I have to take my vacation time instead. I've been seriously considering quitting this company. Since I have medical coverage through my employer, and I am still undergoing treatment, would it be my responsibility to continue paying for my doctor visits, if I do quit my job? Or would the company still pay since treatment began under their policy while I was still employed? - Is this your question? Add additional information