Heat Pumps and Electric Heating - TXV question

I had a restriction in the line last year and it was determined to be the inside txv in the air handler. I have since educated myself in regards to heat pumps and how they operate. The question I have is there a possibility that I only have one txv inside but not one outside at the compressor? I can not see one there. I know what to look for and am wondering if this system just has one. If so would it be smart to have the outside valve added? I have a Ruud 14 Achiever and it is 4 years old. It does have a large evaporator just before the compressor as well. I noted in another post that by air temp drops at the handler about 6 degrees and then slowly recovers, could there be a relationship between the txv and this drop. When I hold the small refrig line at the handler it starts warm gets somewhat cold and the warms up again. Any info on this would be much appreciated.

Just wanted to add that a few weeks ago a tech came out to check everything as a preventative and he said all was well. I just have a feeling that my system is not running efficiently. The liquid line starts warm then in a minutes time you can hear what sounds like a vibration and the liquid line becomes cool. Then the temperature starts rebounding slowly to what it first was and the liquid line warms up as well. For instance, unit comes on to 95 degrees, one minute passes, liquid line grows colder, temp from handler drops 6 to 7 degrees, vibration noise goes away, temp starts increasing a degree each minute, temp reaches 95 degrees again, temp continues to increase depending on outside temp. This doesn't sound right.