Your site does look irritated but not necessarily infected. Showering is fine and is actually good because it will loosen the scab that is there. You don't want to have scabbing in removal sites - this is what creates scars. You want to keep your site clean (even clean with 1/2 peroxide and water), remove any scabs or crusty skin, and then goop it up with Polysporin or Vaseline (and cover if needed). Do this until new pink skin is forming in the site but not crustiness. This will allow the skin too heal much nicer and keep scarring to a minimum.
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while some say you should keep the area dry for the first 24 hours, evidence for these claims is lacking...casual soap, shampoo or conditioner are not a problem...but the area looks a little swollen...might be a good idea to put a warm compress on it several times a day for 10-15 minutes each time...
After a mole is removed it is very important to take proper care to prevent scarring and infection. I often tell my patients to clean with hydrogen peroxide and bacitracin and change the dressing twice a day. If you are worried it is infected please return to your treating physician for examination.
It is safe to shower after mole removal. Do not scrub the area but you can get it wet and then pat dry. You might consider local wound care to help the area heal.