Background Check - Follow up with HR again?

Hi,

I am a senior graduating in May and an incoming analyst at a BB. I accepted the offer in September and did not receive any email about the status of my background check for two months so followed up with HR and was communicated that I should hear back within the next few weeks. Few weeks have passed, and I have yet to hear anything. At this point, I have to start searching for housing and also applying for a work visa, which at max could take up to 6 months process. If I signed the offer contract, should I assume that there won't be any issues with the background check and plan ahead as usual? Should I follow up with the HR, and if so, when would be a reasonable time given that I have already asked her a few weeks ago? For those who have gone through a similar situation, any insight or advice would be much appreciated