First, if you haven't noticed her passing any feces, then constipation must be on the top of our list for your wee one. And if that is the case, this would be something that you can address at home. The offering of foods with high water content would be a good start. Further to that, you can also treat her with a bit of kitty hairball medication (ie. Catalax). This is available from the vet or the pet shop. It works to lubricate the gut and can facilitate the movement of feces out of the rectum. Alternatively, you can administer a small volume of Miralax, lactulose (LINK) or mineral oil orally (ideally offer in food or if given via oral syringe then take care to avoid aspiration, since that would cause problems we'd best avoid) as a GI lubricant. Furthermore, if she is eating you can mix in some canned pumpkin or a pinch of unflavored Metamucil. Just like people, these can restore fecal output regularity. For ease of administering and getting some more fluids/nutrition into her if she is not eating properly, you can give this in veggie babyfood.
Now if she is passing feces, then we have other issues to consider. Because if she is bloated (my concern) but is passing a normal amount of food and feces through her guts, this means that gastrointestinal based disease is less likely for her. That means we may also need to consider conditions of other organs of the abdomen.
The reason I why I had noted that I'd want to know more about her urination is to determine if she is 1) able to urinate (and doesn't have a blocked bladder causing her distress) or 2) if her urination had increased (therefore leading to larger bladders more often, which could be a hint of hormone disease like diabetes or cushings). Otherwise, another issue that is often mistaken for distention and constipation is when the hamster has a cyst or tumor (benign or malignant) within the abdomen. These can arise on any organ within the abdomen (ie kidney, liver, etc). It can also arise from fluid accumulation in the abdomen which can be seen with organ diseases (like those of the heart or liver).And any of these abnormal space occupying lesions can cause a secondary constipation as the weight of the mass/cyst/fluid compresses the non-rigid gut and makes passing feces more difficult for the animal. Therefore, if you think she cannot defecate, they could be underlying reasons as to why.
And as she is a female, we can also see similar issues secondary to disease of the reproductive tract. This can cysts/tumors of the ovaries or uterus. Or we can see uterine infections called pyometra manifest in this manner. In the case of pyometras, we may see pus like discharge at her vulva if it is an open infection but if it is a closed infection then the distension, discomfort, and increased respiration (both by impeding normal diaphragm movement from its taking up space and with secondary metabolic imbalances) may be all we see. In Lucky’s case, without knowing when you last saw any feces or urination and whether she is bloated, we cannot assume it is a primary constipation issue and to consider the other potential differentials. Therefore, it would be ideal to have her seen urgently. Especially so if her respiration is being affected; since a prey species won't show signs of discomfort/illness unless they are just too poorly. That said, if you are sure she is impacted then you can consider trying the above for her to try to get things moving within her gut.
If you try those and do not see improvement, then you will want to follow up with her vet. They will be able to identify which of these is causing her signs or they may be able to pop the ultrasound probe on her belly and tell you if this is fluid (like a cyst or a bladder issue) or if she does have a mass growing in his abdomen. Furthermore, then can rule out uterine infection, which often needs at least antibiotics if not surgery to spay her and remove the infected uterus. Depending on the findings, they will be able to give you an idea if she can be treated and what her overall prognosis is for the long term. But as most of these are quite serious, it would be prudent to be proactive to give her the best chance here.
I hope this information is helpful. Please do let me know if you have any further questions. If you have no further questions, feedback is always appreciated.
All the best,