My joints started hurting and swelling yesterday and it is getting worse. My mother has arthritis and this seems similar but I’m only 33. I did have a cold last week and was wondering if it was possible to get arthritis from my cold?

An acute onset of joint paint affecting many joints and following a viral illness is considered to be viral arthritis which should resolve without complications in days to weeks.
However it is also important to consider early onset rheumatoid arthritis which could present similarly as well as rheumatic fever which affects mainly small joints.  Therefore, a visit to your healthcare provider is warranted if symptoms don’t resolve so proper tests can be performed.