You have the right to sue the hotel but you may have an uphill legal battle. Your first course of action is to speak with management at the hotel let them know you want damages for your injuries, and medical costs. It may be that they will offer you a settlement.
Hotel's are responsible for offering their guests a safe place to stay. As the plaintiff in a lawsuit you have the burden of proof
You were bitten at the hotel. It appears your photo evidence is probably sufficient to establish that fact. However, playing devils advocate you describe only seeing 3 bedbugs, the hotel will argue you were the source of the infestation.
You will need to prove the hotel was aware of a bedbug problem. It may be sufficient to establish the Hotel should have known by virtue of changing the linens etc. Infestations do not occur overnight. This is normally done by interviewing witnesses e.g. prior residents of the room. Staff (if you can get an honest answer from them).
You might be able to subpoena
their bed bug control company to see if your room or other surrounding rooms were treated for an infestation in recent history both prior to and after your stay.
You might be able to determine whether there have been any other lawsuits filed against the hotel for bedbugs. Check the court docket in the county where the hotel is located to see if any other suits have been filed against the hotel.
You will also need to have all of your "evidence" for your attorney ready:
Hotel receipt proving your stay at the hotel
Photos of the room and bedbugs
Photos of the bug bites
Doctor's statement that the bites are bedbug bytes
Costs of treatment
Lists of Witnesses (including other bitten guests you were aware of)
Copy of you hotel bill showing a room change.
Credit card receipts
It is possible to sue the Hotel, but be prepared for a highly contested proceeding. Hotels have insurers and staff attorneys to defend these claims.
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