You indicated it's a company phone. Do you know if they are running any type of endpoint management software on it? i.e. Symantec, Sophos, Blackberry, Ivanti, etc. It's not very common today , but it's certainly a growing part of the IT market.
If they are, depending on the software suite they will know you've loaded unauthorized software and if you've changed any phone wireless or security settings <-- Any exceptions are typically alerted and logged on the management console. They will also have a log of who you called and texted (using the authorized apps), your current software versions, etc.
If you loaded a texting app, used it and then deleted the app, it's not likely that end-point software will know who and what was texted (I'm assuming the app talks to the vendors servers directly using data), unless it uses the standard SMS protocol. It is possible a log or similar remnants of the deleted app could still be on the phone and yes endpoint tools will allow the admin to look through your phone remotely. But most IT people simply don't have the time to do this.
BUT ........ your adding and deleting of a texting app on a regular basis will be logged and is obviously suspicious in-of-itself. Your activities will eventually draw attention depending how security sensitive the company is. <-- Again, if your company doesn't use endpoint software, they won't know anything without touching the phone.