Yes, if you make a claim against your own physical damage coverages, in this case your collision coverage, then it is normal that you must pay the deductible associated with that portion of your policy. It does not matter if you are at fault or not in an accident, if you use your own coverage to make a claim for your vehicle's damages the deductible will be due.

When you are not at fault in an accident and you use your own coverages to repair your vehicle it is normal that your insurance carrier will subrogate, thus go after, the at-fault party or their insurance company for the monies they paid out. Your insurance company may also try to recoup your deductible amount; you will need to speak with your claims department to see if they will try to do so.

Keep in mind since this was a multiple car accident your insurer may not be able to recoup all of their monies let alone your deductible amount. If one person was responsible for the multiple car accident which damaged your vehicle then likely their liability limits will be exceeding in paying out everyone's claims so your insurer may not be able to get back the monies paid out on your side.

If your insurance provider is subrogating to get for the amount of the monies they paid out and your deductible all together then they will typically try their best since they want their monies paid back just as you would like your deductible amount back. The time period it will take for them to receive any money will vary depending such variables as if there is a clear cut at-fault party for them to go after, the limits of the motorist's liability policy, state laws, etc.

Your insurance company may not be able to get back your deductible amount. If that is the case then you may want to check out your state laws to see about going after the at-fault party in court to sue for your deductible amount.