Re: lying on its side, that can be a rabbits simply lounging, which isn’t concerning. If your rabbit is being lethargic (which is not having a lot of energy), then that’s a problem. Most rabbits sleep during the daytime hours, so keep that in mind that it may just be your rabbit trying to sleep.
Re: the sneezing, URIs or upper respiratory infections are common in rabbits. They are typically treated with oral antibiotics, but what can be tricky is finding the right one. My rabbit Wick went through 3 different antibiotics until we found the treatment that worked to stop his sneezing. Pasteurella is one specific bacteria which can cause sneezing, but there are others and trial and error is often the tactic used to figure out what treatment will stick.
How often is the sneezing?
The answers provided in this discussion are for general guideline purposes only. The information is not intended to diagnose or treat your pet. Seek the advice of your veterinarian or a qualified behaviorist.