Can I use regular eye drops between doses of medicated eyedrops for scratchy eyes?

The blink is often impaired for the first few days from the swelling, and your eye will get dry.  This can create a sandy sensation or some itching of the eyes.  I have all of my patients use artificial tears after the surgery along with the eye ointment.  If it doesn't improve, you should see an ophthalmologist.    

Although the Tobradex is a steroid/antibiotic combination.  Some corneas really don't like the antibiotic which can chew up the corneal surface.  There can be other reasons for the scratchiness as well.  I think you indicated in your other post that you are having trouble seeing clearly.  This also points to corneal drying or irritation as a basis for your symptoms. If your surgeon is not board certified in ophthalmology, such as a facial plastic surgeon or general plastic surgeon, they really lack the basic equipment to examine the eye surfaces and determine why your eyes are irritated and the vision blurry.  I could certainly guess what might help your eye comfort but my best advise is have your eyes examined by a cornea specialist or a fellowship trained oculoplastic surgeon.  It might be that you are having a reaction to the tobradex or having some other issue.  Yes, part of the solution might be to use an artificial tear drop.  But without an examination it is just guessing.  Don't guess here.  Call your surgeon and if they can't make the eyes immediately more comfortable consider seeing your general ophthalmologist or one of the subspecialists mentioned.

You can combine artificial tears to help lubricate the eyes while using Tobradex drops.  You should see an ophthalmologist though to identify the cause your scratchy eyes if you haven't already done so.  Are you experiencing post surgical dryness, do you have an infection, could you have a corneal abrasion?  These conditions should be evaluated are treated differently.  Hope you get feeling better soon.