Hi HannahRoseee,
I've had the same experience with my female syrian, I first noticed it by chance really as the blood spots were so small and like you couldn't figure out where it was coming from but she was acting normally. Firstly I would say to definitely take her to the vet as if you're not sure where it's coming from it could be from her reproductive system due to pyometra which female syrians are susceptible too. In my case it wasn't pyometra, just worth a check as it is a serious illness!
After taking my ham to the vets she was given anti-inflammatories and antibiotics as they thought it was a urinary tract infection but this didn't help, and then after a bad experience with that vet and a second opinion, the new vet pretty much told me it would be unfair to put her through any other testing and it didn't appear that she was in pain or losing much blood, so to just monitor her. Overall not the outcome I hoped for, but now I know to stay vigilant in case her circumstances change.
It's probably unlikely you'll have the same experience as me (it was very stressful and involved multiple difficult decisions!!) but certainly worth getting her checked out. They'll most likely do an ultrasound and take a urine sample if they suspect it's coming from her back end.
Some other things you can do in the meantime if you're waiting for an appointment at the vet, try and see if her wee has visible blood in it (a UTI is usually associated with blood in the urine) or any other symptoms (like excessive sneezing, and injuries etc). Also worth weighing her regularly from now on if you don't already, just gives an idea if she starts to not feel well and stops eating!
On a side note, my vet also said carrots can cause orange wee which can look like blood!
Try not to panic, one step at a time and see what the vet has to say! And be comforted by the fact she's not acting unwell, that's at least a sign it's not very serious yet if she is ill