GA pilot reported a near miss during cruise that required them to leave their ATC assigned altitude to avoid a possible collision.

Narrative

I was on an IFR flight plan from ZZZ - ZZZ1; filed altitude was 9;000 via the ZZZZZ SID. After departing ZZZ I was instructed to fly a north easterly heading and assigned an altitude of 2;000ft. Around the XA:50 am time ATC advised me of traffic (Aircraft Y) ahead on my route 500ft below. His advisory call out of the traffic also said something along the lines of 'I can't do anything for you about it'. I advised him I was looking for the traffic; but I never had the traffic insight. I had the traffic on my TAS/ADS-B in the airplane but did not have him visually. As we got closer and closer I still did not have the traffic in sight and recognized we were on a direct course to collide with each other. The traffic had now started a climb from 1500ft to 2000ft. My aircraft was at 2000ft and on the same heading and altitude that was instructed by ATC. I recognized that if I stayed on the instructed altitude that was assigned; I would collide with the incoming aircraft. At this point I tried to queue up my mic to ask ATC for a deviation to avoid the traffic; but he was extremely busy and I could not get a word in. After a Traffic advisory notification of traffic at the same altitude from the TAS/ADS-B in the airplane; I disconnected the autopilot and pitched the nose up to avoid the traffic that I still could not see. This resulted in a climb to 2500ft that I immediately notified ATC of as soon as possible. This climb was something that I had to do to protect the safety of flight and avoid a collision with the other aircraft. This all happened very fast; and ATC was notified of the change of altitude as quickly as possible. ATC then instructed me to make a turn to a north westerly heading and descend and maintain 2000ft which was also immediately complied with. After the incident the controller asked me something along the lines of 'Did you get a resolution advisory?'; and he also asked something along the lines of 'Have you been in this airspace before?; That is how we do things here'. Our aircraft was not equipped with Resolution Advisories so I instructed him that we did not get an RA. At this point the traffic was no longer a factor and I continued my flight as instructed by ATC and landed safely at ZZZ1.Ultimately I felt that this was a situation that ATC did not expect. I felt the controller got busy with other aircraft and did not notice that the other aircraft had started a climb to my same altitude. After a traffic advisory alert from my aircraft I felt that I needed to take immediate action in order to avoid a collision. My airplane was doing 160 knots while the incoming Aircraft Y was doing 100 knots. If action was not taken immediately; I felt that the aircraft's would collide within the next 15-30 seconds. Ultimately the safety of flight should take precedent over ATC instruction.