This is wrong. Many existing viruses affect the vascular system. For example, the influenza vaccine is one of the strongest interventions we have to prevent cardiovascular mortality.

https://pubmed.ncbi.nlm.nih.gov/23474244/#:~:text=A%20spectrum%20of%20cardiovascular%20complications,exacerbation%20of%20existing%20cardiovascular%20disease.

Vascular effects are also not the explanation of varied symptoms. Here's a short excerpt regarding colds and their symptoms.

>The symptoms of the common cold appear to result from release of cytokines and other mediators from infected nasal epithelial cells and from an influx of polymorphonuclear cells (PMNs). Nasal washings of volunteers experimentally infected with rhinovirus showed a 100-fold increase in PMN concentration 1 to 2 days after inoculation.20 The influx of PMNs coincides with the onset of symptoms and correlates with a colored nasal discharge.21 A yellow or white nasal discharge may result from the higher number of PMNs, whereas the enzymatic activity of PMNs (due to myeloperoxidase and other enzymes) may cause a green nasal discharge.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7152197/