Well, that's very confusing. You will need to be able to log into myCIC to retrieve the medical request. Cohabitation is assessed before the stage you are at ('Eligibility'). Since you have passed that stage (which is why your Sponsor's side shows DM, and your side shows 'In Process'), they've already assessed that.
At the stage you are in, they are assessing: Medical (which sounds like you may need to redo), Criminality (which they can do very quickly), and Security (usually this is the hold up in this stage). So it's hard to assess how long from here because you control the timing on the Medical, and they cannot control the processing time on the Security screening (conducted by CSIS on behalf of CBSA). 3-6 mos is common (but could be done quicker, depending on your past travel history).