There are a variety of over the counter products to suppress coughs. I do not recommend using them to qualify for donating blood. It does not look like taking them would increase one's eligibility to donate blood. Taking antibiotics will disqualify you.
Red Cross guidelines on blood donation:Allergy, Stuffy Nose, Itchy Eyes, Dry Cough
Accept as long as person feels well, no fever, and no problems breathing through mouth Antibiotics
Wait 2 days after taking antibiotics for an infection.
Accept persons taking antibiotics to prevent an infection, for example, following dental procedures or for acne.
Those with a temperature above 99F may not donate until the fever is passed.Cold, Flu, Sore Throat
Wait if you have a fever or a productive cough.
Wait if you feel unwell on the day of donation.
Wait 2 days after you have completed antibiotic treatment for sinus, throat or lung infection.Hemoglobin, Hematocrit, Blood Count
Each donor's hemoglobin is measured at the blood collection site before donation is allowed. The level required for blood donation is set by the Food and Drug Administration for all blood collections in the United States. It is common for donors, especially women, to have hemoglobin levels too low to donate. This is sometimes due to iron deficiency, but may also be normal for the person. If you are disqualified as a donor because of a low blood count, you may return and try again at any time.
Accept those with a hemoglobin at or above 12.5 g/dL.
Accept those with a hematocrit at or above 38%.Medications
In almost all cases, medications do not disqualify a person as a blood donor. The person's eligibility is based on the reason that the medication was prescribed. As long as the condition is under control and the person is healthy, blood donation is usually permitted. There are just a few selected drugs that are potentially toxic if given to a patient through transfusion; persons on these medications have waiting periods before donating:
Wait 3 years from the last dose of Soriatane (acitretin).
Wait 4 weeks after taking Accutane (isoretinoin) Proscar (finasteride),Propecia (finasteride), methotrexate
Persons who have ever taken Tegison (etretinate) are not eligible to donate blood.
Wait 3 months after taking Arava (leflunomide).
Wait 5 days after taking coumadin.
Wait 36 hours after taking aspirin, Plavix (clopidogrel) or Ticlid (ticlopidine)if you are going to donate plateletpheresis.