Can traces of blood, show up in urine test (uti test), a week before your period?

Unlikely: It is unlikely to see blood traces in your urine a whole week before a period. During your period and up to 3 days after, it is usual to see traces of blood in your urine.

No: It is very common for small amounts of microscopic blood to be detected on a simple urine test (dipstick). I normally recommend people not to worry too much about it but not to ignore it. Get a repeat urine test in 2-3 weeks (once your period has finished). If you still have blood on the test at that stage then it may be worth looking further into.