Can you have contamination OCD but not have a cleaning compulsion?

Both my therapist and my psychiatrist agree that I display moderate obsessive-compulsive behaviors (don't know if they've given me the actual disorder). The two instances in which this behavior occurs is kinda of one in the same and also not. The first, which is a behavior I've had since childhood, is an obsession and phobia of skin infections and bumps. However, I've never taken extra precautions with cleaning my hands or my skin (with the exception of if I've touched aomething I consider infectious, even if it's not, like acne. Then I'm crying because no amount of cleaning will get my skin clean). Instead, I will pick and scratch and dig into my skin until its bleeding because blood means that it's clean (yes, I know this doesn't make sense and actually makes me more prone to skin infections).

The second instance, which has only started recently, occurrd after I had two mice in my apartments. I became really paranoid of mites and bed bugs infesting my bedroom. When I found a beetle on my pillow one night, I completely flipped out and started crying and was unable to sleep. I kept feeling like bugs were clawing all over my skin and that they were going to bite me and lay eggs in my skin, causing bumps and holes. But, again, while I eventually washed my sheets, that wasn't what I needed to do to get the thoughts to stop. I had to keep getting up and checking my skin and scratching at anything that seemed abnormal. I also now have to check ever inch of my covers and take out any spots on it, which are always lint or whatnot. I recently found a house centipede on the wall of my bedroom and started hyperventilating and crying. I wasn't able to sleep until 6am, and even then I woke up at 8am.

But I'm just confused, I guess, because shouldn't the compulsion be to clean? Like, isn't that the "rational" compulsion that will actually help get rid of the problems? Is it still OCD/OCS if it's compulsive checking?

Edit: Also for the infection fears via bugs, I've taken to wearing bug repellent on my arms and sleeping as far away from the walls as possible. It just feels like nowhere with fabric is safe, which sucks since my apartment is carpetted. I just sort of feel like I'm losing my mind here.

Edit 2: I now have cleaning compulsions after adopting a cat with a minor flea and worm problem. I have washed my sheets 3 times in thr last 7 days but haven't been able to sleep on them. I've treated my carpet with three different chemicals (diatamaceous earth, a different flea-carpet powder, and a flea-killing spray). Everything still feels contaminated and dirty and infested. Anything that has touched caroet although she was only in my bedroom for 30 minutes max before being quarantined in the bathroom. Now I have to wash up to my elbows and change my clothes everytime I exit the room with the cat.