Really you shouldn’t have any antibiotics left over from last time as you are supposed to finish the full course… however…
NO is the short answer, you should not take the Trimethoprim for these symptoms as you don’t have a full course available for one and therefore will be running the risk of allowing the bug to gain immunity to the antibiotic and secondly you don’t know for absolute sure that you do have a UTI.
Make a GPs appointment, get a proper diagnosis and get a proper prescription and if it is for antibiotics be sure to finish the FULL course this time. Antibiotics aren’t supposed to be taken just until you feel better but right up until the very last tablet is finished (no left overs!!)
Hope you feel better soon,