How long will I feel like I have sand in my eyes?

Feeling Dry the first few days is common. Curiously, it's less common in my hands when the patient (dry or not) uses unpreserved tears or Thera-tears 4 times a day for a month before the surgery.Almost everyone recommends aggressive lubrication afterwards and the dryness tends to resolved within a few weeks in almost everyone. For patients over 30 and smokers, the dryness can last longer. Some doctors use punctal plugs, steroid drops, Restasis (cyclosporin), ointments, or Xiidra. I feel they don't work all that great compared to a cheaper option. The cheaper and better option, in my opinion is unfrozen autologous serum tears. The problem is usually 90% better in 2 weeks. The unfrozen serum tears rarely need to be used for more than 2 months.

Having gritty sandy eyes after lasik is completely normal. The bulk of the irritation is gone in the first 24 hours. It then drops down to a low level sandy feeling which can last days to weeks. In general most patients by week one are doing very well and tell me they don't feel anything. I overtreat dry eyes after surgery and force everyone to get preservative free artificial tears and put them in every 2-3 hours while awake. Although it's annoying, I know my patients are keeping their corneas lubricated and my results will be excellent. Preservative free drops come in little vials (as opposed to the drops that come in reusable bottles). They are extremely safe for your eyes and you can take an "eye bath" in them without causing a problem. Drops with preservative can cause eye irritation and pain when used more than about 3-4 times per day. 
You are still early in your postop period so I am sure you will do fantastic! 

The dryness that causes the "sand-in-the-eye" feeling does vary quite a bit from patient to patient.  Make sure that you are using plenty of artificial tears to keep the eye as hydrated as possible.  If the artificial tears you are using aren't seeming to help, you may consider switching to a different brand of rewetting drops.