My 7 week old baby has a rash that looks likes someone got a red pen and dotted her, what can this be? She also has a cold that she had for 2 weeks

Viral rash? Many viruses (even cold viruses) can have associated rashes. However, in babies under 2 months of age i wouldn't wait a long time to find out what's going on. If she has been acting fine otherwise (eating well, not fussy or excessively sleepy), you can wait a day or two and see if it just fades away. If not, have your pediatrician look at it on monday to determine it's nothing more.
M.D. visit. From the description of the rash it may be a viral infection. Her cold symptoms should have resolved by day 10. At day 14 of a cold, even without fever, she should be checked. Other possibilities include a reaction to lotion or soap. I would advise switching to white dove and eucerin/nivea without added fragrance.